Deep learning can solve differential equations, and differential equations can model deep learning. What have we learned and where to next?
The focus of this workshop is on the interplay between deep learning (DL) and differential equations (DEs). In recent years, there has been a rapid increase of machine learning applications in computational sciences, with some of the most impressive results at the interface of DL and DEs. These successes have widespread implications, as DEs are among the most well-understood tools for the mathematical analysis of scientific knowledge, and they are fundamental building blocks for mathematical models in engineering, finance, and the natural sciences. This relationship is mutually beneficial. DL techniques have been used in a variety of ways to dramatically enhance the effectiveness of DE solvers and computer simulations. Conversely, DEs have also been used as mathematical models of the neural architectures and training algorithms arising in DL.
This workshop will aim to bring together researchers from each discipline to encourage intellectual exchanges and cultivate relationships between the two communities. The scope of the workshop will include important topics at the intersection of DL and DEs.
| Introduction and opening remarks (Introduction) | |
| Weinan E - Machine Learning and PDEs (Invited Talk) | |
| NeurInt-Learning Interpolation by Neural ODEs (Spotlight Talk) | |
| Neural ODE Processes: A Short Summary (Spotlight Talk) | |
| Neha Yadav - Deep learning methods for solving differential equations (Invited Talk) | |
| Coffee Break (Break) | |
| GRAND: Graph Neural Diffusion (Spotlight Talk) | |
| Neural Solvers for Fast and Accurate Numerical Optimal Control (Spotlight Talk) | |
| Non Vanishing Gradients for Arbitrarily Deep Neural Networks: a Hamiltonian System Approach (Poster) | |
| GRAND: Graph Neural Diffusion (Poster) | |
| Performance-Guaranteed ODE Solvers with Complexity-Informed Neural Networks (Poster) | |
| On Second Order Behaviour in Augmented Neural ODEs: A Short Summary (Poster) | |
| Layer-Parallel Training of Residual Networks with Auxiliary Variables (Poster) | |
| Actor-Critic Algorithm for High-dimensional PDEs (Poster) | |
| Statistical Numerical PDE : Fast Rate, Neural Scaling Law and When it’s Optimal (Poster) | |
| Scaling physics-informed neural networks to large domains by using domain decomposition (Poster) | |
| Neural ODE Processes: A Short Summary (Poster) | |
| MGIC: Multigrid-in-Channels Neural Network Architectures (Poster) | |
| HyperPINN: Learning parameterized differential equations with physics-informed hypernetworks (Poster) | |
| Investigating the Role of Overparameterization While Solving the Pendulum with DeepONets (Poster) | |
| Enhancing the trainability and expressivity of deep MLPs with globally orthogonal initialization (Poster) | |
| Learning Dynamics from Noisy Measurements using Deep Learning with a Runge-Kutta Constraint (Poster) | |
| Poster Session 1 (Poster Session) | |
| Empirics on the expressiveness of Randomized Signature (Poster) | |
| Gotta Go Fast with Score-Based Generative Models (Poster) | |
| Quantized convolutional neural networks through the lens of partial differential equations (Poster) | |
| Philipp Grohs - The Theory-to-Practice Gap in Deep Learning (Invited Talk) | |
| Lunch Break (Break) | |
| Deep Reinforcement Learning for Online Control of Stochastic Partial Differential Equations (Spotlight Talk) | |
| Statistical Numerical PDE : Fast Rate, Neural Scaling Law and When it’s Optimal (Spotlight Talk) | |
| Coffee Break (Break) | |
| Neural Solvers for Fast and Accurate Numerical Optimal Control (Poster) | |
| Fitting Regularized Population Dynamics with Neural Differential Equations (Poster) | |
| Learning Implicit PDE Integration with Linear Implicit Layers (Poster) | |
| Multigrid-augmented deep learning preconditioners for the Helmholtz equation (Poster) | |
| A neural multilevel method for high-dimensional parametric PDEs (Poster) | |
| Poster Session 2 (Poster Session) | |
| Deep Reinforcement Learning for Online Control of Stochastic Partial Differential Equations (Poster) | |
| Shape-Tailored Deep Neural Networks With PDEs (Poster) | |
| Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based ROMs (Poster) | |
| Data-driven Taylor-Galerkin finite-element scheme for convection problems (Poster) | |
| NeurInt-Learning Interpolation by Neural ODEs (Poster) | |
| Sparse Gaussian Processes for Stochastic Differential Equations (Poster) | |
| Expressive Power of Randomized Signature (Poster) | |
| Adversarial Sampling for Solving Differential Equations with Neural Networks (Poster) | |
| Spectral PINNs: Fast Uncertainty Propagation with Physics-Informed Neural Networks (Poster) | |
| Uncertainty Quantification in Neural Differential Equations (Poster) | |
| Accelerated PDEs for Construction and Theoretical Analysis of an SGD Extension (Poster) | |
| Anima Anandkumar - Neural operator: A new paradigm for learning PDEs (Invited Talk) | |
| HyperPINN: Learning parameterized differential equations with physics-informed hypernetworks (Spotlight Talk) | |
| Learning Implicit PDE Integration with Linear Implicit Layers (Spotlight Talk) | |
| Solving Differential Equations with Deep Learning: State of the Art and Future Directions (Panel Discussion) | |
| Final Remarks | |