Workshop
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 · Thorsteinn Jonsson · Animesh Garg · Murtadha Aldeer
Tue 14 Dec, 3:45 a.m. PST
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.
Schedule
Tue 3:45 a.m. - 4:00 a.m.
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Introduction and opening remarks
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Introduction
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SlidesLive Video |
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Tue 4:00 a.m. - 4:45 a.m.
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Weinan E - Machine Learning and PDEs
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Invited Talk
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link
SlidesLive Video |
Weinan E 🔗 |
Tue 4:45 a.m. - 5:00 a.m.
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NeurInt-Learning Interpolation by Neural ODEs
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Spotlight Talk
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SlidesLive Video |
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Tue 5:00 a.m. - 5:15 a.m.
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Neural ODE Processes: A Short Summary
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Spotlight Talk
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SlidesLive Video |
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Tue 5:15 a.m. - 6:00 a.m.
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Neha Yadav - Deep learning methods for solving differential equations
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Invited Talk
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link
SlidesLive Video |
Neha Yadav 🔗 |
Tue 6:00 a.m. - 6:15 a.m.
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Coffee Break
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Tue 6:15 a.m. - 6:30 a.m.
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GRAND: Graph Neural Diffusion
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Spotlight Talk
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SlidesLive Video |
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Tue 6:30 a.m. - 6:45 a.m.
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Neural Solvers for Fast and Accurate Numerical Optimal Control
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Spotlight Talk
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SlidesLive Video |
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Tue 6:45 a.m. - 7:30 a.m.
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Poster Session 1
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Poster Session
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Tue 6:45 a.m. - 7:30 a.m.
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GRAND: Graph Neural Diffusion ( Poster ) > link | Benjamin Chamberlain · James Rowbottom · Maria Gorinova · Stefan Webb · Emanuele Rossi · Michael Bronstein 🔗 |
Tue 6:45 a.m. - 7:30 a.m.
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Empirics on the expressiveness of Randomized Signature ( Poster ) > link | Enea Monzio Compagnoni · Luca Biggio · Antonio Orvieto 🔗 |
Tue 6:45 a.m. - 7:30 a.m.
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Enhancing the trainability and expressivity of deep MLPs with globally orthogonal initialization ( Poster ) > link | Hanwen Wang · Paris Perdikaris 🔗 |
Tue 6:45 a.m. - 7:30 a.m.
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Gotta Go Fast with Score-Based Generative Models ( Poster ) > link | Alexia Jolicoeur-Martineau · Ke Li · Rémi Piché-Taillefer · Tal Kachman · Ioannis Mitliagkas 🔗 |
Tue 6:45 a.m. - 7:30 a.m.
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Quantized convolutional neural networks through the lens of partial differential equations ( Poster ) > link | Ido Ben-Yair · Moshe Eliasof · Eran Treister 🔗 |
Tue 6:45 a.m. - 7:30 a.m.
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MGIC: Multigrid-in-Channels Neural Network Architectures ( Poster ) > link | Moshe Eliasof · Jonathan Ephrath · Lars Ruthotto · Eran Treister 🔗 |
Tue 6:45 a.m. - 7:30 a.m.
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HyperPINN: Learning parameterized differential equations with physics-informed hypernetworks ( Poster ) > link | · Fei Sha 🔗 |
Tue 6:45 a.m. - 7:30 a.m.
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Learning Dynamics from Noisy Measurements using Deep Learning with a Runge-Kutta Constraint ( Poster ) > link | Pawan Goyal · Peter Benner 🔗 |
Tue 6:45 a.m. - 7:30 a.m.
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Investigating the Role of Overparameterization While Solving the Pendulum with DeepONets ( Poster ) > link | Pulkit Gopalani · Anirbit Mukherjee 🔗 |
Tue 6:45 a.m. - 7:30 a.m.
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Non Vanishing Gradients for Arbitrarily Deep Neural Networks: a Hamiltonian System Approach ( Poster ) > link | Clara Galimberti · Luca Furieri 🔗 |
Tue 6:45 a.m. - 7:30 a.m.
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Performance-Guaranteed ODE Solvers with Complexity-Informed Neural Networks ( Poster ) > link | Feng Zhao · Xiang Chen · Jun Wang · Zuoqiang Shi · Shao-Lun Huang 🔗 |
Tue 6:45 a.m. - 7:30 a.m.
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Neural ODE Processes: A Short Summary ( Poster ) > link | Alexander Norcliffe · Cristian Bodnar · Ben Day · Jacob Moss · Pietro Lió 🔗 |
Tue 6:45 a.m. - 7:30 a.m.
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On Second Order Behaviour in Augmented Neural ODEs: A Short Summary ( Poster ) > link | Alexander Norcliffe · Cristian Bodnar · Ben Day · Nikola Simidjievski · Pietro Lió 🔗 |
Tue 6:45 a.m. - 7:30 a.m.
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Layer-Parallel Training of Residual Networks with Auxiliary Variables ( Poster ) > link | Qi Sun · Hexin Dong · Zewei Chen · WeiZhen Dian · Jiacheng Sun · Yitong Sun · Zhenguo Li · Bin Dong 🔗 |
Tue 6:45 a.m. - 7:30 a.m.
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Statistical Numerical PDE : Fast Rate, Neural Scaling Law and When it’s Optimal ( Poster ) > link | Yiping Lu · Haoxuan Chen · Jianfeng Lu · Lexing Ying · Jose Blanchet 🔗 |
Tue 6:45 a.m. - 7:30 a.m.
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Actor-Critic Algorithm for High-dimensional PDEs ( Poster ) > link | Xiaohan Zhang 🔗 |
Tue 6:45 a.m. - 7:30 a.m.
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Scaling physics-informed neural networks to large domains by using domain decomposition ( Poster ) > link | Ben Moseley · Andrew Markham 🔗 |
Tue 7:30 a.m. - 8:15 a.m.
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Philipp Grohs - The Theory-to-Practice Gap in Deep Learning ( Invited Talk ) > link | Philipp Grohs 🔗 |
Tue 8:15 a.m. - 10:45 a.m.
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Lunch Break
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Tue 10:45 a.m. - 11:00 a.m.
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Deep Reinforcement Learning for Online Control of Stochastic Partial Differential Equations
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Spotlight Talk
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SlidesLive Video |
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Tue 11:00 a.m. - 11:15 a.m.
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Statistical Numerical PDE : Fast Rate, Neural Scaling Law and When it’s Optimal
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Spotlight Talk
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SlidesLive Video |
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Tue 11:15 a.m. - 11:30 a.m.
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Coffee Break
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Tue 11:30 a.m. - 12:15 p.m.
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Poster Session 2
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Poster Session
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Tue 11:30 a.m. - 12:15 p.m.
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Adversarial Sampling for Solving Differential Equations with Neural Networks ( Poster ) > link | Kshitij Parwani · Pavlos Protopapas 🔗 |
Tue 11:30 a.m. - 12:15 p.m.
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Spectral PINNs: Fast Uncertainty Propagation with Physics-Informed Neural Networks ( Poster ) > link | Björn Lütjens · Mark Veillette · Dava Newman 🔗 |
Tue 11:30 a.m. - 12:15 p.m.
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Uncertainty Quantification in Neural Differential Equations ( Poster ) > link | Olga Graf · Pablo Flores · Pavlos Protopapas 🔗 |
Tue 11:30 a.m. - 12:15 p.m.
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Multigrid-augmented deep learning preconditioners for the Helmholtz equation ( Poster ) > link | Yael Azulay · Eran Treister 🔗 |
Tue 11:30 a.m. - 12:15 p.m.
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Deep Reinforcement Learning for Online Control of Stochastic Partial Differential Equations ( Poster ) > link | Erfan Pirmorad · Farnam Mansouri · Amir-massoud Farahmand 🔗 |
Tue 11:30 a.m. - 12:15 p.m.
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Accelerated PDEs for Construction and Theoretical Analysis of an SGD Extension ( Poster ) > link | Yuxin Sun · Dong Lao · Ganesh Sundaramoorthi · Anthony Yezzi 🔗 |
Tue 11:30 a.m. - 12:15 p.m.
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Shape-Tailored Deep Neural Networks With PDEs ( Poster ) > link | Naeemullah Khan · Angira Sharma · Philip Torr · Ganesh Sundaramoorthi 🔗 |
Tue 11:30 a.m. - 12:15 p.m.
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Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based ROMs ( Poster ) > link | Stefania Fresca · Federico Fatone · Andrea Manzoni 🔗 |
Tue 11:30 a.m. - 12:15 p.m.
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Data-driven Taylor-Galerkin finite-element scheme for convection problems ( Poster ) > link | Luciano DROZDA 🔗 |
Tue 11:30 a.m. - 12:15 p.m.
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NeurInt-Learning Interpolation by Neural ODEs ( Poster ) > link | Avinandan Bose · Aniket Das · Yatin Dandi · Piyush Rai 🔗 |
Tue 11:30 a.m. - 12:15 p.m.
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Learning Implicit PDE Integration with Linear Implicit Layers ( Poster ) > link | Marcel Nonnenmacher · David Greenberg 🔗 |
Tue 11:30 a.m. - 12:15 p.m.
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Neural Solvers for Fast and Accurate Numerical Optimal Control ( Poster ) > link | Federico Berto · Stefano Massaroli · Michael Poli · Jinkyoo Park 🔗 |
Tue 11:30 a.m. - 12:15 p.m.
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Fitting Regularized Population Dynamics with Neural Differential Equations ( Poster ) > link | David Calhas · Rui Henriques 🔗 |
Tue 11:30 a.m. - 12:15 p.m.
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A neural multilevel method for high-dimensional parametric PDEs ( Poster ) > link | Cosmas Heiß · Ingo Gühring · Martin Eigel 🔗 |
Tue 11:30 a.m. - 12:15 p.m.
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Sparse Gaussian Processes for Stochastic Differential Equations ( Poster ) > link | Prakhar Verma · Vincent ADAM · Arno Solin 🔗 |
Tue 11:30 a.m. - 12:15 p.m.
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Expressive Power of Randomized Signature ( Poster ) > link | Lukas Gonon · Josef Teichmann 🔗 |
Tue 12:15 p.m. - 1:00 p.m.
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Anima Anandkumar - Neural operator: A new paradigm for learning PDEs
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Invited Talk
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link
SlidesLive Video |
Animashree Anandkumar 🔗 |
Tue 1:00 p.m. - 1:15 p.m.
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HyperPINN: Learning parameterized differential equations with physics-informed hypernetworks
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Spotlight Talk
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SlidesLive Video |
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Tue 1:15 p.m. - 1:30 p.m.
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Learning Implicit PDE Integration with Linear Implicit Layers
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Spotlight Talk
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SlidesLive Video |
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Tue 8:00 p.m. - 8:58 p.m.
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Solving Differential Equations with Deep Learning: State of the Art and Future Directions
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Panel Discussion
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Tue 8:58 p.m. - 8:59 p.m.
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Final Remarks
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Final Remarks
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