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25.04:24
4:15 PM | Two cases of using machine learning in mathematical modelling
Ekaterina Muravleva, Skoltech (Moscow)
In this talk I will describe two topics. First part is devoted to how generative models can be used for 2D to 3D reconstruction problem (with application to digital rock analysis).In the second part I will overview our recent paper that uses neural operators to learn nonlinear preconditioners (coupled with a flexible iterative solver). | Robert Scheichl | Mathematikon, SRA | | | | |
18.04.24
4:15 PM
| Phinli: a physics informed surrogate model for elliptic PDEs and its Bayesian inverse problem analysis
J Andrés Christen (CIMAT-CONAHCYT, México)
The talk addresses Bayesian inferences in inverse problems with uncertainty quantification involving a computationally expensive forward map associated with solving a partial differential equations. To mitigate the computational cost, the paper proposes a new surrogate model informed by the physics of the problem, specifically when the forward map involves solving a linear elliptic partial differential equation. The study establishes the consistency of the posterior distribution for this surrogate model and demonstrates its effectiveness through numerical examples with synthetic data. The results indicate a substantial improvement in computational speed, reducing the processing time from several months with the exact forward map to a few minutes, while maintaining negligible loss of accuracy in the posterior distribution. | Rob Scheichl | INF 205 Mathematikon, Seminarraum A | | | | |
12.04.24
1 PM -2 PM | Simulation-based inference and the places it takes us
Prof. Jakob Macke (Uni Tübingen)
Many fields of science make extensive use of mechanistic forward models which are implemented through numerical simulators. Simulation-based inference aims to make it possible to perform Bayesian inference on such models by only using model-simulations, but not requiring access to likelihood evaluations. I will speak about recent work on developing simulation based inference methods using flexible density estimators parameterised with neural networks, on improving their robustness and efficiency, and applications to modelling problems in neuroscience, computational imaging and astrophysics. Finally, I will talk about the prospect of building large-scale models of neural circuits in the Drosophila melanogster by combing connectomics and simulation-based machine learning. | CZS Heidelberg Initiative for Model-Based AI | Seminar Room A + B (0.202 + 0.203), Mathematikon,
INF 205, Heidelberg | | | | |
12.04.24
9:30 AM - 11 AM | Practical Equivariances via Relational Conditional Neural Processes
Dr. Manuel Haussmann, University of Southern Denmark
Conditional Neural Processes (CNPs) are a class of meta-learning models popular for combining the runtime efficiency of amortized inference with reliable uncertainty quantification. Many relevant machine learning tasks, such as in spatiotemporal modeling, Bayesian Optimization, and continuous control, inherently contain equivariances – for example to translation – which the model can exploit for maximal performance. However, prior attempts to include equivariances in CNPs do not scale effectively beyond two input dimensions.
In this talk, I will introduce the theory behind CNPs and discuss our recent proposal on how to incorporate equivariances into any neural process model and how we can ensure scalability to higher dimensions. | Fred Hamprecht | INF 205 Mathematikon
Seminarraum 10 | | | | |
19.03.24
11:15 AM - 12:15 AM | Topologically penalized regression on manifolds
Wolfgang Polonik, UC Davis
We study a regression problem on a compact manifold. In order to take advantage of the underlying geometry and topology of the data, we propose to perform the regression task on the basis of eigenfunctions of the Laplace-Beltrami operator of the manifold that are regularized with topological penalties. We will discuss the approach and the penalties, provide some supporting theory and illustrate the performance of the methodology on some data sets, illustrating the relevance of our approach in the case where the target function is ``topologically smooth”. This is joint work with O. Hacquard, K. Balasubramanian, G. Blanchard and C. Levrard. | Enno Mammen | SR 8 (4th floor) | | | | |
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12.03.24
10 AM - 11 AM | Semi-supervised learning: The provable benefits of unlabeled data for sparse Gaussian classification
Boaz Nadler, Weizmann Institute of Science, Israel
The premise of semi-supervised learning (SSL) is that combining labeled and unlabeled data enables learning significantly more accurate models. Despite empirical successes, the theoretical understanding of SSL is still far from complete. In this talk, we consider SSL for high dimensional sparse Gaussian classification. A key challenge here is feature selection, detecting the few variables informative for the classification problem.
For this SSL setting, we derive information theoretic lower bounds as well as computational lower bounds, based on the low-degree likelihood ratio framework. Our key contribution is the identification of a regime in the problem parameters (dimension, sparsity, number of labeled and unlabeled samples) where a polynomial time SSL algorithm that we propose succeeds, but any computationally efficient supervised or unsupervised schemes, that separately use only the labeled or unlabeled data would fail. This result highlights the provable benefits of combining labeled and unlabeled data for feature selection in high dimensions.
| Fred Hamprecht | SR 8 (4th floor) | | | | |
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| Multiscale exploration of single cell data with geometric harmonic analysis
Prof. Guy Wolf, Université de Montréal, Canada
High-throughput data collection technologies are becoming increasingly common in many fields, especially in biomedical applications involving single cell data (e.g., scRNA-seq and CyTOF). These introduce a rising need for exploratory analysis to reveal and understand hidden structure in the collected (high-dimensional) Big Data. A crucial aspect in such analysis is the separation of intrinsic data geometry from data distribution, as (a) the latter is typically biased by collection artifacts and data availability, and (b) rare subpopulations and sparse transitions between meta-stable states are often of great interest in biomedical data analysis. In this talk, I will show several tools that leverage manifold learning, graph signal processing, and harmonic analysis for biomedical (in particular, genomic/proteomic) data exploration, with emphasis on visualization, data generation/augmentation, and nonlinear feature extraction. A common thread in the presented tools is the construction of a data-driven diffusion geometry that both captures intrinsic structure in data and provides a generalization of Fourier harmonics on it. These, in turn, are used to process data features along the data geometry for interpretability, denoising, and generative purposes. Finally, I will demonstrate the application of the resulting tools in biomedical applications, such as early embryoid body development and COVID 19 mortality.
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19.02.24
12:45 PM - 5 PM | HI4AI – Human Intelligence for Artificial Intelligence in Medicine
Digital patient twins embody virtual representations of patients based on health and environmental data to model individual and population behavior for improving health care by guidance through artificial intelligence (AI). The thematic research network (TRN) HI4AI extends this concept by the digital clinician twin. It aims to foster inter- and transdisciplinary communication to gain new insight into clinical reasoning/human intelligence (HI) to enable its effective support by AI.
Program
12:45 – 13:00 Coffee & Registration
13:00 – 13:45 Introduction to the TRN
PD. Dr. Holger A. Lindner (Experimental Anesthesiology, UMM):
HI4AI in medicine - overview
Prof. Dr. Stefan Riezler (Statistical NLP, IWR):
Grounding large language models in clinical
measurements and expert knowledge
Prof. Dr. Jan Rummel (Experimental Psychology
and Cognitive Self-Regulation):
Self-regulation of cognition
Prof. Dr. Vera Araujo-Soares (CPD):
The role of co-design and process evaluation for
future implementation
13:45 – 14:30 Spotlight talks
• AI ethics
- PD Dr. Markus Herrmann (NCT):
AI ethics and medical decision making
• Medical decision support by AI
- M.Sc. Markus Buchwald (EMCL, IWR):
Learning to defer
• Hospital admission and outpatient care
- Dipl.-Inform. Sebastian Schöning
(Fraunhofer IPA): TBA
- Prof. Emanuel Schwarz, Ph.D. (ZI):
Advancing personalized psychiatry through
artificial intelligence
• Acute care
- Intensive care, TBA
• Chronic medical conditions
- PD Dr. med. Sebastian Belle (Transl.
Oncology, UMM):
Automation process in endoscopic adenoma therapy -optimized long-term therapy strategies
14:30 – 14:50 Coffee break
14:50 – 15:40 Breakout discussions
• Hospital admission and outpatient care
• Acute care
• Chronic medical conditions
15:40 – 16:00 Coffee break
16:00 – 16:45 Results from breakout discussions
• Hospital admission and outpatient care
• Acute care
• Chronic medical conditions
16:45 – 17:00 Résumé: expectations, gaps & collaborative next steps
Lindner, Riezler, Rummel, Araujo-Soares
Registration
The TRN HI4AI invites participation of stakeholders across diverse disciplines. If you are interested in contributing to this network, please apply by email to PD Dr. Holger Lindner
holger.lindner@medma.uni-heidelberg.de with “HI4AI” in the subject line and
● state in 80 words or less your motivation and
● indicate the order of your preference for participation in one of the Breakout Discussions:
- Hospital admission and outpatient care
- Acute care
- Chronic medical conditions
● On-site child care may be offered by the Medical Faculty Mannheim depending on the demand. Please indicate your interest.
Registration Deadline: January 31st, 2024 Please note that participation is limited.
| Organized by PD Dr. Holger A. Lindner, Prof. Stefan Riezler, Prof. Jan Rummel, Prof. Vera Araujo-Soares, PD. Dr. Dr. Verena-Schneider-Lindner, Christopher Jones, M.Sc.
Funded by the Federal Ministry of Education and Research (BMBF) and the Ministry of Science Baden-Württemberg within the framework of the Excellence Strategy of the Federal and State
| CUBEX ONE, Mannheim Medical Technology Campus
Franz Volhard Straße 5, 68167 Mannheim | | | | |
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| Geometric-harmonic data exploration
Prof. Guy Wolf,
CIFAR AI Chair at MILA, Montreal, and Associate Professor at Université de Montréal.
The pretalk starts at 1 pm and will be held by Prof. Fred Hamprecht.
High-throughput data collection technologies are becoming increasingly common in many fields, especially in biomedical applications involving single cell data (e.g., scRNA-seq and CyTOF). These introduce a rising need for exploratory analysis to reveal and understand hidden structure in the collected (high-dimensional) Big Data. A crucial aspect in such analysis is the separation of intrinsic data geometry from data distribution, as (a) the latter is typically biased by collection artifacts and data availability, and (b) rare subpopulations and sparse transitions between meta-stable states are often of great interest in biomedical data analysis. In this talk, I will show several tools that leverage manifold learning, graph signal processing, and harmonic analysis for biomedical (in particular, genomic/proteomic) data exploration, with emphasis on visualization, data generation/augmentation, and nonlinear feature extraction. A common thread in the presented tools is the construction of a data-driven diffusion geometry that both captures intrinsic structure in data and provides a generalization of Fourier harmonics on it. These, in turn, are used to process data features along the data geometry for interpretability, denoising, and generative purposes. Finally, time permitting, I will relate this approach to the geometric scattering transform that generalizes Mallat's scattering to non-Euclidean domains and provides a mathematical framework for theoretical understanding of geometric deep learning. | | | | | | | |
01.02.24
2:15 PM | Coarse-grained molecular dynamics for proteins with neural networks: Challenges and breakthroughs
Aleksander Durumeric, Freie Universität Berlin
Neural network force-fields have enabled molecular dynamics (MD) simulations at unprecedented accuracy by efficiently emulating expensive ab initio calculations. However, these advances have not yet accelerated the long-timescale modelling of biomolecular complexes, where the computational cost of classical force-fields is difficult to reduce. One leading approach for adapting neural network force fields to this context focuses on creating force-fields at a reduced (i.e. coarse-grained) resolution. We here discuss how this task differs from that at the atomistic resolution and discuss recent advances by myself and colleagues which have brought the idea of an accurate and extrapolative neural network protein coarse-grained force-fields within reach, with focus on the collection and processing of training data. | Tristan Berau | Institute for Theoretical Physics Philosophenweg 19, Seminar Room | | | | |
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| Bayesian Inference Models for Healthcare Resilience:
Insights and Lessons from Mexico’s COVID-19 Response
Prof. Antonio Capella Kort Instituto de Matemáticas Universidad Nacional Autónoma de México
Navigating the challenges of the global COVID-19 pandemic required strategic decisions tailored to each country’s unique circumstances. In less developed nations, the threat of overwhelming hospital capacity was especially severe. Rather than building scenarios based on mathematical models, our team used a dynamic forecasting approach. We developed a series of models that provided 4-week probabilistic forecasts, complete with uncertainty quantification. These forecasts, crucially informed by real-time data, predicted the demand for hospital beds and ventilators, which served as the backbone for decisions and public policies adopted by federal health authorities in Mexico from April 2020 to January 2022. The journey was a challenging one. An incompletely characterized virus and the unpredictable dynamics of societal behavior made crafting a useful model difficult.
In this talk, I will present a retrospective of these models and critically review their objectives, successes, and limitations. Our methodology and modeling decisions will be presented, from the intricacies of data used for model fitting to the balance between model complexity and parameter identifiability. The predictive power and performance of our models will also be reviewed. Beyond the algorithms and forecasts, I’ll share our experiences collaborating with health authorities and communicating with the general public. Discover the highs and lows, the challenges faced, and the insights we gained. | | | | | | | |
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11.01.24
2.15 PM | Machine Learning in condensed matter: from molecules and materials to quantum systems
Huziel E. Sauceda, Universidad Nacional Autonoma de Mexico
Machine learning (ML) encompasses a wide range of algorithms and models, which have been prominently applied to condensed matter. Some applications range from atomistic simulations, generative quantum and classical distributions, predictors of physicochemical properties, differential equations’ ansatz, among many others. In this talk, we will present some examples of how ML models have advanced our understanding of molecular systems and their complex interactions. In particular, we will focus on how combining machine learned force fields and quantum interatomic dilation, not only reveals the intricate nature of molecular systems, but also shows the limitations of many electronic structure methods. Additionally, we will briefly show some of the current applications of ML to quantum systems in our group, this with particular emphasis to describe excited states in second quantized representation and their paramount importance while describing experimental results. | Tristan Bereau | Institute for Theoretical Physics, Philosophenweg 19, Seminar room | | | | |
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11.12.23
9:30 AM -11 AM | Enhancing Accuracy in Deep Learning Using Random Matrix Theory
L. Berlyand, Penn State, USA
We discuss applications of random matrix theory (RMT) to the training of deep neural networks (DNNs). Our focus is on pruning of DNN parameters, guided by the Marchenko-Pastur spectral approach. Our numerical results show that this pruning leads to a drastic reduction of parameters while not reducing the accuracy of DNNs and CNNs. Moreover, pruning the fully connected DNNs actually increases the accuracy and decreases the variance for random initializations. We next show how these RMT techniques can be used to remove 20% of parameters from state-of-the-art DNNs such as Resnet and VIT while reducing accuracy by at most 2% and, at some instances, even increasing accuracy.
Finally, we provide a theoretical understanding of these results by proving the Pruning Theorem that establishes a rigorous relation between the accuracy of the pruned and non-pruned DNNs.
Joint work with E. Sandier (U. Paris 12), Y. Shmalo (PSU student) and L. Zhang (Jiao Tong U.) | IWR
Fred Hamprecht | Mathematikon
Im Neuenheimer Feld 205
Konferenzraum / 5. Stock, Raum 5/104
69210 Heidelberg | | | | |
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| NCT Data Science Seminar
Integrative data analysis by combining networks, dynamical models and machine learning
Katharina Baum, FU Berlin, Hasso Plattner Institute, Icahn School of Medicine at Mount Sinai
Combining different views from complementary data layers is key for robust predictions in biomedical research. However, it is still challenging to incorporate dependencies and relationships into coherent modeling and prediction frameworks, especially when applying machine learning (ML). I focus on two approaches that I combine with ML: Network-based methods allow for representing and harnessing the interaction of entities and data layers, and dynamical models can represent temporal properties and intricate dependencies of the investigated processes. In this talk, I will present recent examples of our developed methods for integrative data analysis. These range from differential integrated multi-omics networks, over neural networks with (multi-)graph input, to infusing prior knowledge from dynamical models into ML. We tackle problems such as drug response prediction or epidemic time series forecasting in scenarios with sparse data. | | | | | | | |
| About Vision and Language models: What grounded linguistic phenomena do they understand? How much do they use the image and text modality?
Letitia Parcalabescu, Department of Computational Linguistics, Heidelberg University
In this talk, we will introduce Vision and Language (VL) models which can very well say if an image and text are related and answer questions about images. While performance on these tasks is important, task-centered evaluation does not tell us why they are so good at these tasks, such as what are the fine-grained linguistic capabilities of VL models use when solving them. Therefore, we present our work on the VALSE💃 benchmark to test six specific linguistic phenomena grounded in images. Our zero-shot experiments with five widely-used pretrained VL models suggest that current VL models have considerable difficulty addressing most phenomena. In the second part, we ask how much a VL model uses the image and text modality in each sample or dataset. To measure the contribution of each modality in a VL model, we developed MM-SHAP which we applied in two ways: (1) to compare VL models for their average degree of multimodality, and (2) to measure for individual models the contribution of individual modalities for different tasks and datasets. Experiments with six VL models on four VL tasks highlight that unimodal collapse can occur to different degrees and in different directions, contradicting the wide-spread assumption that unimodal collapse is one-sided. | | | | | | | |
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| STRUCTURES Jour Fixe
Holger Fröning with Pretalk by Guido Kanschat
On Accelerating Deep and Bayesian Neural Architectures
Deep artificial neural networks are a prominent approach for decision-making in scenarios involving uncertainty. These networks have significantly enhanced performance in various prediction tasks, such as image recognition, speech processing, and signal analysis. However, their utilization demands substantial computational resources and memory. On the other hand, there is a growing need to implement machine learning techniques on resource-constrained devices, including Internet of Things (IoT) devices, edge devices, and mobile platforms. In this talk, we will start by examining prior research focused on accelerating Deep Neural Networks (DNNs) through compression techniques, particularly quantization, pruning, and architecture optimization. While DNNs excel at operating under uncertainty, they are incapable of reasoning about uncertainty itself. Detecting situations where a neural architecture cannot provide a well-founded prediction is crucial. Consequently, probabilistic models have recently garnered significant interest. We will provide a brief overview of these models and discuss potential avenues to address their substantially increased computational demands. | | | | | | | |
24.10.2023 | Minisymposium:
Mathematical Data Science and Optimization
09:00 AM Konstantin Rusch (Massachusetts Institute of Technology, ETH Zurich)
Physics-inspired Machine Learning
Combining physics with machine learning is a rapidly growing field of research.Thereby, most work focuses on leveraging machine learning methods to solve problemsin physics. Here, however, we focus on the converse, i.e., physics-inspired machinelearning, which can be described as incorporating structure from physical systems intomachine learning methods to obtain models with better inductive biases. More concretely,we propose several physics-inspired deep learning architectures for sequencemodelling based on nonlinear coupled oscillators, Hamiltonian systems and multi-scaledynamical systems. The proposed architectures tackle central problems in the field ofrecurrent sequence modeling, namely the vanishing and exploding gradients problemas well as the issue of insufficient expressive power. Moreover, we discuss physicsinspiredlearning on graphs, wherein the dynamics of the message-passing propagationare derived from physical systems. We further prove that these methods mitigate theover-smoothing issue, thereby enabling the construction of deep graph neural networks(GNNs). We extensively test all proposed methods on a variety of versatile syntheticand real-world datasets, ranging from image recognition, speech recognition, naturallanguage processing (NLP), medical applications, and scientific computing for sequencemodels, to citation networks, computational chemistry applications, and networks of articles and websites for graph learning models.
10:00 AM Johannes Hertrich (TU Berlin)
Sliced MMD Gradient Flows with Negative Distance Kernel for Generative Modeling and Inverse Problems
We consider gradient flows with respect to the maximum mean discrepancy (MMD) with negative distance kernel, which is also known as energy distance. In order to achieve computational efficiency, we prove that for certain kernels the MMD coincides with its sliced version. Therefore, all computations can be performed in a one-dimensional setting, where the MMD with negative distance kernel can be evaluated by a simple sorting algorithm with improved computational complexity. This enables us to simulate MMD particle flows in high dimensions for a large number of particles. We approximate these particle flows by neural networks and apply them for generative modeling and posterior sampling in Bayesian inverse problems. From a theoretical viewpoint, we study Wasserstein gradient flows with respect to our MMD functionals. Interestingly, particles might "explode" in this setting, i.e., the flow turns atomic measures into absolutely continuous ones and vice versa. We analytically derive the Wasserstein flows for some special cases and propose a numerical approximation of suitable forward and backward time discretizations by generative neural networks.
02:00 PM Johannes Wiesel (Carnegie Mellon University)
The out-of-sample prediction error of the square-root lasso and related estimators
We study the classical problem of predicting an outcome variable, Y, using a linear combination of a d-dimensional covariate vector, X. We are interested in linear predictors whose coefficients solve: inf_β (E[(Y - < β, X >)^r])^(1/r) + 𝛿 || β ||, where r >1 and d > 0 is a regularisation parameter. We provide conditions under which linear predictors based on these estimators minimize the worst-case prediction error over a ball of distributions determined by a type of max-sliced Wasserstein metric. A detailed analysis of the statistical properties of this metric yields a simple recommendation for the choice of regularization parameter. The suggested order of 𝛿, after a suitable normalization of the covariates, is typically d/n, up to logarithmic factors. Our recommendation is computationally straightforward to implement, pivotal, has provable out-of-sample performance guarantees, and does not rely on sparsity assumptions about the true data generating process.
03:00 PM Caroline Geiersbach (WIAS Berlin)
Stochastic Algorithms for Physics-Based Systems under Uncertainty
In this talk, I will present a class of problems from stochastic optimization, where the constraints contain a family of partial differential equations (PDEs). These problems have a wide range of applications, from engineering, to materials science, to economics. One central challenge is that analysis of these systems typically needs to be done in infinite dimensions; optimization theory is delicate due to the function space setting. Optimization procedures need to account for numerical error from the discretization of the PDE. When solving these systems using stochastic algorithms, error due to the stochastic dimension also needs to be correctly controlled. I will focus on the usage of the stochastic gradient method for solving various problems in this class and discuss what is known about convergence and efficiency. There are many perspectives for this topic. Recent developments in the field of data science can be carried over to the infinite-dimensional context. Vice versa, the problems studied in physics-based systems present new challenges for data science. | Jan Johannes | Uni Heidelberg,
Mathematikon Raum 5.104,
Im Neuenheimer Feld 205, 69120 Heidelberg | | | | |
23.10.24 | Minisymposium:
Mathematical Data Science and Optimization
09:00 AM Johannes Maly (University of Munich)
Explicit regularization, implicit bias, and the effect of quantization
A core challenge in mathematical data science is to understand and leverage intrinsic structures of sets. With reference to different branches of my research I will describe how in the last decade the focus shifted from explicit structural regularization in inverse problems and related fields to implicit regularization in massively overparametrized machine learning models. I will furthermore discuss the effect of coarse quantization, i.e., representation of real numbers by a finite alphabet of small size, on established results. The parts of my work that will serve as illustration encompass compressed sensing, covariance estimation from one-bit samples, and the implicit bias of gradient descent in matrix factorization and regression problems.
10:00 AM Lisa Kreusser (University of Bath)
Unlocking the Full Potential of Data: From Applied Analysis and Optimisation to Applications
Recent and rapid breakthroughs in contemporary biology, climate science, and data science have unveiled a spectrum of intricate mathematical challenges which can be tackled through the fusion of applied and numerical analysis, as well as optimisation. In this talk, I will begin by delving into a class of interacting particle models with anisotropic interaction forces and their corresponding continuum limit. These models find their inspiration in the simulation of fingerprint patterns, which play a critical role in databases in forensic science and biometric applications. I will showcase our recent findings, including the development of a mean-field optimal control algorithm to tackle an inverse problem arising in parameter identification. Transitioning from interaction-focused models to the realm of transport networks, I will introduce an optimization approach tailored for a unique coupling of differential equations that arises in the context of biological network formation. Additionally, I will provide insights into my recent research in data science, encompassing topics such as image segmentation, non-convex optimisation algorithms for machine learning, generative models such as Wasserstein Generative Adversarial Networks (WGANs), and semi-supervised learning techniques. Finally, I will give an overview of ongoing projects that explore the synergies between optimisation, numerical analysis and data science. These projects include optimisation algorithms designed for training deep neural networks, the development of robust machine learning algorithms for differential equations, the study of physics-informed generative models, the rigorous investigation of score-based diffusion models, and the design of data assimilation algorithms for uncertain models.
02:00 PM Jakob Zech (Heidelberg University)
Neural operator surrogates
In this talk we discuss the use of neural network based operator surrogates to approximate smooth maps between infinite-dimensional Hilbert spaces. Such surrogates have a wide range of applications and can be used in uncertainty quantification and parameter estimation problems in fields such as classical mechanics, fluid mechanics, electrodynamics, earth sciences etc. In this case, the operator input represents the problem configuration and models initial conditions, material properties, forcing terms and/or the domain of a partial differential equation (PDE) describing the underlying physics. The output of the operator is the corresponding PDE solution. We will also present an alternative approach using interpolation, which allows for deterministic construction and eliminates the need for training the network weights. In both cases, algebraic and dimension-independent convergence rates are obtained.
03:00 PM Diyora Salimova (University of Freiburg)
Deep neural network approximations for partial differential equations
Most of the numerical approximation methods for partial differential equations (PDEs) in the scientific literature suffer from the so-called curse of dimensionality (CoD) in the sense that the number of computational operations and/or the number of parameters employed in the corresponding approximation scheme grows exponentially in the PDE dimension and/or the reciprocal of the desired approximation precision. Recently, certain deep learning-based approximation methods for PDEs have been proposed and various numerical simulations for such methods suggest that deep neural network (DNN) approximations might have the capacity to indeed overcome the CoD in the sense that the number of real parameters used to describe the approximating DNNs grows at most polynomially in both the PDE dimension and the reciprocal of the prescribed approximation accuracy. In this talk, we show that solutions of suitable Kolmogorov PDEs can be approximated by DNNs without the CoD.
| Jan Johannes | Uni Heidelberg,
Mathematikon Raum 5.104,
Im Neuenheimer Feld 205, 69120 Heidelberg | | | | |
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| AI InScide Out Unconference
This event offers the opportunity for leading scientists in AI applied to health, life, and natural sciences to meet and to have interdisciplinary exchanges. Join us for a vibrant community meeting that will bring together AI scientists in the areas of bioinformatics, imaging, structural biology, physics (and more), to stimulate new collaborations and spark boundary-pushing discussions. AI InScide Out will feature keynote talks from distinguished scientists, presentations from researchers associated with AI Health Innovation Cluster and ELLIS-Life Heidelberg, and flash talks from submitted abstracts. The unconference session will be distinct from a regular conference, providing ample opportunities for scientific exchange and informal discussions among all participants. We invite researchers from all career stages to register. You will have the opportunity to present your own work, either focused on a scientific advance, failure and challenge, or novel opportunities for scientific questions that are ready to be tackled using AI. The event is free of charge but registration is mandatory. Please register online by September 15: https://indico.dkfz.de/e/ai. Admission will be on a first come first-serve basis with priority given to submissions that include a (short) scientific abstract. | | | | | | | |
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| Workshop CoE STRUCTURES and MRA Cognitive Science (FoF4) Human Intelligence (HI) meets Artificial Intelligence (AI) Join us for a day with many opportunities to get in touch with Cognitive Science/Field of Focus 4 and STRUCTURES, meet new colleagues and collaborators, discuss science with keynote speakers, and to network. We are very happy to welcome researchers at all career stages (doctoral students, post docs, professors) and especially those faculty members who joined Heidelberg University only recently and who are interested to build new transdisciplinary collaborations in the context of HI meets AI. Topics could be e.g. cognitive and computational neuroscience, the computational mind, neural networks, superstatistics, dynamical systems... All these topics are of interest for cognitive research, AI and neuroscience, and at the same time potentially also for other fields like data and computer sciences, mathematics, microbiology, technology development and medical sciences. Other fields and field suggestions are very welcome! This in-person 2-days workshop will cover many aspects of this emerging field of research, and will combine insights into exciting current research activities and key discoveries with the development of a future perspective for Cognitive Science, HI and AI. A program andmore details will follow during the next weeks. We are very much looking forward to a day with stimulating presentations and discussion in an enjoyable atmosphere. | | | | | | | |
| NCT Data Science Seminar: QI DOU Image-Based Robotic Surgery Intelligence Department of Computer Science & Engineering at The Chinese University of Hong Kong
With rapid advancements in medicine and engineering technologies, the operating room has evolved to a highly complex environment, where surgeons take advantage of computers, endoscopes and robots to perform procedures with more precision while less incision. Intelligence, together with its authorized cognitive assistance, smart data analytics, and automation, is envisaged to be a core fuel to transform next-generation robotic surgery in numerous known or unknown exciting ways. In this talk, I will present ideas, methodologies and applications of image-based robotic surgery intelligence from three perspectives, i.e., AI-enabled surgical situation awareness to improve surgical procedures, AI-powered large-scale data analysis to enhance surgical education, AI-driven multi-sensory perception to achieve surgical subtask automation.. | | | | | | | |
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| 5th Summer School in Medical Physics 2023:
Data Science and Machine Learning in Radiotherapy
This summer school is a hybrid event and is subdivided into an online phase and a hybrid phase (attendance phase or live online phase). participants can decide to follow the course online and on site or 100% virtually. The online phase with pre-recorded lectures introduces the basics in machine learning, focusing on 3D voxelized geometries, its most frequent applications, and methodological as well as ethical aspects. The live online and attendance phases will then expose how machine learning may interfere radiotherapy workflows in detail. The knowledge of deep learning methodologies for image synthesis, organ and target segmentation, and image registration in the context of radiotherapy will be expanded. Furthermore, applications in computational dosimetry and plan optimization will be discussed, ranging from dose prediction, guided plan optimization, and treatment outcome prediction. The summer school is designed for PhD/MD, MSc or BSc students. More information is available on our website: http://www.dkfz.de/summer_school2023_de.
Registration necessary:Y es
Registration deadline: 06/15/2023
Registration: https://www.dkfz.de/en/medphys/education_and_training/summer_school_2023_de.html | | | | | | | |
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| GIS Colloquium – Talks (Summer Term 2023)
GeoAI Research and Technology Transfer for National Mapping
Dr. Samantha T. Arundel, Center of Excellence for Geospatial Information Science, US Geological Survey, USA
GeoAI Research and Technology Transfer for National Mapping" highlights the application of Artificial Intelligence (AI) and Geographic Information Systems (GIS) for national mapping. The presentation emphasizes the use of GeoAI technology for efficient and accurate data acquisition, processing, and analysis in the GIS, Cartography and Mapping fields. Dr. Arundel will discuss the potential benefits of AI in mapping, such as reduced costs, increased accuracy, and faster mapping processes. The presentation also discusses various applications of GeoAI technology, such as image recognition, object detection, and optical character recognition (OCR). Of particular emphasis is the importance of partnerships between research institutions and government agencies to promote the adoption of AI technology in mapping. Finally, the presentation showcases some examples of successful implementation of GeoAI technology in national mapping, including the use of AI for feature extraction from various types of imagery, noise reduction in point-clouds, and OCR for knowledge extraction from historical maps. | | | | | | | |
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06.07.23
4pm | How to enhance chemical databases for atomistic machine learning?
Luis Itza Vazquez-Salazar, University of Basel
Machine learning (ML) has revolutionized the field of atomistic simulations. It is now possible to obtain high-quality predictions of chemical properties at a low computational cost. Given that the computational effort to evaluate such a statistical model is independent of the quality of the input data, the most significant bottleneck for devising yet better ML models is the considerable amount of data required to train them. Although the community consensus is that more data naturally leads to better performance, it has been found that this working hypothesis is not necessarily correct for predicting chemical properties. Consequently, there is a need to identify how to obtain suitable data for training ML models while retaining the best performance of the model.
In this contribution, we will discuss the use of uncertainty quantification (UQ) methods for atomistic neural networks, such as Deep Evidential Regression and Regression Prior Networks, for identifying outliers in chemical space. Furthermore, results from using different data augmentation (DA) methods like sampling from conformational space and the Atom-in-Molecule (AMONS) fragments to improve the prediction of specific chemical moieties will be discussed. Additionally, the application of UQ techniques to potential energy surfaces will be illustrated. Combining UQ and DA methods set the stage for a workflow to obtain more robust and data-efficient chemical databases while retaining prediction accuracy. | Tristan Bereau | Philosophenweg 19, 69120 Heidelberg, seminar room | | | | |
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| GIS Colloquium – Talks (Summer Term 2023)
Spatial Optimization, Significance and Evolving GIScience
Prof. Dr. Alan T. Murray, Department of Geography, University of California at Santa Barbara, CA 93106, USA
Spatial optimization is introduced and reviewed in historical terms. The significance of spatial optimization is demonstrated through current analysis, management, planning and policy contexts focused on emergency response, food production, wildfire risk mitigation and public health monitoring.
Further, mathematical formalization in spatial optimization offers a theoretical framework to establish findings as significant. The ways in which GIScience perspectives can directly and indirectly support spatial optimization are highlighted. | | | | | | | |
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