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Workshop
Tue Dec 14 03:45 AM -- 08:59 PM (PST)
The Symbiosis of Deep Learning and Differential Equations
Luca Celotti · Kelly Buchanan · Jorge Ortiz · Patrick Kidger · Stefano Massaroli · Michael Poli · Lily Hu · Ermal Rrapaj · Martin Magill · Thor Jonsson · Animesh Garg · Murtadha Aldeer





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)
MGIC: Multigrid-in-Channels Neural Network Architectures (Poster)
Non Vanishing Gradients for Arbitrarily Deep Neural Networks: a Hamiltonian System Approach (Poster)
Performance-Guaranteed ODE Solvers with Complexity-Informed Neural Networks (Poster)
HyperPINN: Learning parameterized differential equations with physics-informed hypernetworks (Poster)
Actor-Critic Algorithm for High-dimensional PDEs (Poster)
Learning Dynamics from Noisy Measurements using Deep Learning with a Runge-Kutta Constraint (Poster)
Quantized convolutional neural networks through the lens of partial differential equations (Poster)
Neural ODE Processes: A Short Summary (Poster)
On Second Order Behaviour in Augmented Neural ODEs: A Short Summary (Poster)
Enhancing the trainability and expressivity of deep MLPs with globally orthogonal initialization (Poster)
Poster Session 1 (Poster Session)
Gotta Go Fast with Score-Based Generative Models (Poster)
Statistical Numerical PDE : Fast Rate, Neural Scaling Law and When it’s Optimal (Poster)
Layer-Parallel Training of Residual Networks with Auxiliary Variables (Poster)
Investigating the Role of Overparameterization While Solving the Pendulum with DeepONets (Poster)
Empirics on the expressiveness of Randomized Signature (Poster)
GRAND: Graph Neural Diffusion (Poster)
Scaling physics-informed neural networks to large domains by using domain decomposition (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)
Uncertainty Quantification in Neural Differential Equations (Poster)
Learning Implicit PDE Integration with Linear Implicit Layers (Poster)
NeurInt-Learning Interpolation by Neural ODEs (Poster)
Deep Reinforcement Learning for Online Control of Stochastic Partial Differential Equations (Poster)
Sparse Gaussian Processes for Stochastic Differential Equations (Poster)
Shape-Tailored Deep Neural Networks With PDEs (Poster)
Fitting Regularized Population Dynamics with Neural Differential Equations (Poster)
Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based ROMs (Poster)
Accelerated PDEs for Construction and Theoretical Analysis of an SGD Extension (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)
Multigrid-augmented deep learning preconditioners for the Helmholtz equation (Poster)
A neural multilevel method for high-dimensional parametric PDEs (Poster)
Neural Solvers for Fast and Accurate Numerical Optimal Control (Poster)
Poster Session 2 (Poster Session)
Data-driven Taylor-Galerkin finite-element scheme for convection problems (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