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Physics-Based Deep Learning

The following collection of materials targets "Physics-Based Deep Learning" (PBDL), i.e., the field of methods with combinations of physical modeling and deep learning (DL) techniques. Here, DL will typically refer to methods based on artificial neural networks. The general direction of PBDL represents a very active and quickly growing field of research.

If you're interested in a comprehensive overview, please check our digital PBDL book: https://www.physicsbaseddeeplearning.org/ (or as PDF: https://arxiv.org/pdf/2109.05237.pdf)

An overview of categories of physics-based deep learning methods

Within this area, we can distinguish a variety of different physics-based approaches, from targeting designs, constraints, combined methods, and optimizations to applications. More specifically, all approaches either target forward simulations (predicting state or temporal evolution) or inverse problems (e.g., obtaining a parametrization for a physical system from observations). Apart from forward or inverse, the type of integration between learning and physics gives a means for categorizing different methods:

  • Data-driven: the data is produced by a physical system (real or simulated), but no further interaction exists.

  • Loss-terms: the physical dynamics (or parts thereof) are encoded in the loss function, typically in the form of differentiable operations. The learning process can repeatedly evaluate the loss, and usually receives gradients from a PDE-based formulation.

  • Interleaved: the full physical simulation is interleaved and combined with an output from a deep neural network; this requires a fully differentiable simulator and represents the tightest coupling between the physical system and the learning process. Interleaved approaches are especially important for temporal evolutions, where they can yield an estimate of future behavior of the dynamics.

Thus, methods can be roughly categorized in terms of forward versus inverse solve, and how tightly the physical model is integrated into the optimization loop that trains the deep neural network. Here, especially approaches that leverage differentiable physics allow for very tight integration of deep learning and numerical simulations.

This repository collects links to works on deep learning algorithms for physics problems, with a particular emphasis on fluid flow, i.e., Navier-Stokes related problems. It primarily collects links to the work of the I15 lab at TUM, as well as miscellaneous works from other groups. This is by no means a complete list, so let us know if you come across additional papers in this area. We intentionally also focus on works from the deep learning field, not machine learning in general.

An example flow result from tempoGAN

I15 Physics-based Deep Learning Links

Flow Matching for Posterior Inference with Simulator Feedback , PDF: https://arxiv.org/pdf/2410.22573

APEBench: A Benchmark for Autoregressive Neural Emulators of PDEs , PDF: http://arxiv.org/pdf/2411.00180

Deep learning-based predictive modelling of transonic flow over an aerofoil , PDF: https://arxiv.org/pdf/2403.17131

ConFIG: Towards Conflict-free Training of Physics Informed Neural Networks , Project: https://tum-pbs.github.io/ConFIG/

The Unreasonable Effectiveness of Solving Inverse Problems with Neural Networks , PDF: http://arxiv.org/pdf/2408.08119

Phiflow: Differentiable Simulations for PyTorch, TensorFlow and Jax , PDF: https://openreview.net/pdf/36503358a4f388f00d587a0257c13ba2a4656098.pdf

How Temporal Unrolling Supports Neural Physics Simulators , PDF: https://arxiv.org/pdf/2402.12971

Stabilizing Backpropagation Through Time to Learn Complex Physics , PDF: https://openreview.net/forum?id=bozbTTWcaw

Symmetric Basis Convolutions for Learning Lagrangian Fluid Mechanics , PDF: https://openreview.net/forum?id=HKgRwNhI9R

Uncertainty-aware Surrogate Models for Airfoil Flow Simulations with Denoising Diffusion Probabilistic Models , Project: https://github.com/tum-pbs/Diffusion-based-Flow-Prediction

Turbulent Flow Simulation using Autoregressive Conditional Diffusion Models , Project: https://github.com/tum-pbs/autoreg-pde-diffusion

Physics-Preserving AI-Accelerated Simulations of Plasma Turbulence , PDF: https://arxiv.org/pdf/2309.16400>

Unsteady Cylinder Wakes from Arbitrary Bodies with Differentiable Physics-Assisted Neural Network , Project: https://github.com/tum-pbs/DiffPhys-CylinderWakeFlow

Score Matching via Differentiable Physics , Project: https://github.com/tum-pbs/SMDP

Guaranteed Conservation of Momentum for Learning Particle-based Fluid Dynamics , Project: https://github.com/tum-pbs/DMCF

Learned Turbulence Modelling with Differentiable Fluid Solvers , Project: https://github.com/tum-pbs/differentiable-piso

Half-Inverse Gradients for Physical Deep Learning , Project: https://github.com/tum-pbs/half-inverse-gradients

Reviving Autoencoder Pretraining (Previously: Data-driven Regularization via Racecar Training for Generalizing Neural Networks), Project: https://github.com/tum-pbs/racecar

Realistic galaxy images and improved robustness in machine learning tasks from generative modelling , PDF: https://arxiv.org/pdf/2203.11956

Hybrid Neural Network PDE Solvers for Reacting Flows , Project: https://github.com/tum-pbs/Hybrid-Solver-for-Reactive-Flows

Scale-invariant Learning by Physics Inversion (formerly "Physical Gradients") , Project: https://github.com/tum-pbs/SIP

High-accuracy transonic RANS Flow Predictions with Deep Neural Networks , Project: https://github.com/tum-pbs/coord-trans-encoding

Learning Meaningful Controls for Fluids , Project: https://rachelcmy.github.io/den2vel/

Global Transport for Fluid Reconstruction with Learned Self-Supervision , Project: https://ge.in.tum.de/publications/2021-franz-globtrans

Solver-in-the-Loop: Learning from Differentiable Physics to Interact with Iterative PDE-Solvers , Project: https://github.com/tum-pbs/Solver-in-the-Loop

Numerical investigation of minimum drag profiles in laminar flow using deep learning surrogates , PDF: https://arxiv.org/pdf/2009.14339

Purely data-driven medium-range weather forecasting achieves comparable skill to physical models at similar resolution , PDF: https://arxiv.org/pdf/2008.08626

Latent Space Subdivision: Stable and Controllable Time Predictions for Fluid Flow , Project: https://ge.in.tum.de/publications/2020-lssubdiv-wiewel

WeatherBench: A benchmark dataset for data-driven weather forecasting , Project: https://github.com/pangeo-data/WeatherBench

Learning Similarity Metrics for Numerical Simulations (LSiM) , Project: https://ge.in.tum.de/publications/2020-lsim-kohl

Learning to Control PDEs with Differentiable Physics , Project: https://ge.in.tum.de/publications/2020-iclr-holl

Lagrangian Fluid Simulation with Continuous Convolutions , PDF: https://openreview.net/forum?id=B1lDoJSYDH

Tranquil-Clouds: Neural Networks for Learning Temporally Coherent Features in Point Clouds , Project: https://ge.in.tum.de/publications/2020-iclr-prantl/

ScalarFlow: A Large-Scale Volumetric Data Set of Real-world Scalar Transport Flows for Computer Animation and Machine Learning , Project: https://ge.in.tum.de/publications/2019-tog-eckert/

tempoGAN: A Temporally Coherent, Volumetric GAN for Super-resolution Fluid Flow , Project: https://ge.in.tum.de/publications/tempogan/

Deep Fluids: A Generative Network for Parameterized Fluid Simulations , Project: http://www.byungsoo.me/project/deep-fluids/

Latent-space Physics: Towards Learning the Temporal Evolution of Fluid Flow , Project: https://ge.in.tum.de/publications/latent-space-physics/

A Multi-Pass GAN for Fluid Flow Super-Resolution , PDF: https://ge.in.tum.de/publications/2019-multi-pass-gan/

A Study of Deep Learning Methods for Reynolds-Averaged Navier-Stokes Simulations , Project: https://github.com/thunil/Deep-Flow-Prediction

Data-Driven Synthesis of Smoke Flows with CNN-based Feature Descriptors , Project: http://ge.in.tum.de/publications/2017-sig-chu/

Liquid Splash Modeling with Neural Networks , Project: https://ge.in.tum.de/publications/2018-mlflip-um/

Generating Liquid Simulations with Deformation-aware Neural Networks , Project: https://ge.in.tum.de/publications/2017-prantl-defonn/

Additional Links for Fluids

Data-Efficient Inference of Neural Fluid Fields via SciML Foundation Model , PDF: https://arxiv.org/abs/2412.13897

DeepLag: Discovering Deep Lagrangian Dynamics for Intuitive Fluid Prediction , PDF: https://arxiv.org/pdf/2402.02425

Inferring Hybrid Neural Fluid Fields from Videos , PDF: https://openreview.net/pdf?id=kRdaTkaBwC

LagrangeBench: A Lagrangian Fluid Mechanics Benchmarking Suite , Project: https://github.com/tumaer/lagrangebench

CFDBench: A Comprehensive Benchmark for Machine Learning Methods in Fluid Dynamics , PDF: https://arxiv.org/pdf/2310.05963.pdf

Physics-guided training of GAN to improve accuracy in airfoil design synthesis , PDF: https://arxiv.org/pdf/2308.10038

A probabilistic, data-driven closure model for RANS simulations with aleatoric, model uncertainty , PDF: https://arxiv.org/pdf/2307.02432

Differentiable Turbulence , PDF: https://arxiv.org/pdf/2307.03683

Super-resolving sparse observations in partial differential equations: A physics-constrained convolutional neural network approach , PDF: https://arxiv.org/pdf/2306.10990

Reduced-order modeling of fluid flows with transformers , PDF: https://pubs.aip.org/aip/pof/article/35/5/057126/2891586

Machine learning enhanced real-time aerodynamic forces prediction based on sparse pressure sensor inputs , PDF: https://arxiv.org/pdf/2305.09199

Reconstructing Turbulent Flows Using Physics-Aware Spatio-Temporal Dynamics and Test-Time Refinement , PDF: https://arxiv.org/pdf/2304.12130

Inferring Fluid Dynamics via Inverse Rendering , PDF: https://arxiv.org/pdf/2304.04446

Multi-scale rotation-equivariant graph neural networks for unsteady Eulerian fluid dynamics , WWW: https://aip.scitation.org/doi/10.1063/5.0097679

AirfRANS: High Fidelity Computational Fluid Dynamics Dataset for Approximating Reynolds-Averaged Navier-Stokes Solutions , PDF: https://arxiv.org/pdf/2212.07564

Exploring Physical Latent Spaces for Deep Learning , PDF: https://arxiv.org/pdf/2211.11298

Modelling spatiotemporal turbulent dynamics with the convolutional autoencoder echo state network , PDF: https://arxiv.org/pdf/2211.11379

Combined space-time reduced-order model with 3D deep convolution for extrapolating fluid dynamics , PDF: https://arxiv.org/pdf/2211.00307

NeuroFluid: Fluid Dynamics Grounding with Particle-Driven Neural Radiance Fields , Project: https://github.com/syguan96/NeuroFluid

Lagrangian Large Eddy Simulations via Physics Informed Machine Learning , PDF: https://arxiv.org/pdf/2207.04012

Learning to Estimate and Refine Fluid Motion with Physical Dynamics , PDF: https://arxiv.org/pdf/2206.10480.pdf

Deep Reinforcement Learning for Turbulence Modeling in Large Eddy Simulations , PDF: https://arxiv.org/pdf/2206.11038

Physics-Embedded Neural Networks: Graph Neural PDE Solvers with Mixed Boundary Conditions , PDF: https://arxiv.org/pdf/2205.11912

Physics Informed Neural Fields for Smoke Reconstruction with Sparse Data , Project: https://rachelcmy.github.io/pinf_smoke/

Leveraging Stochastic Predictions of Bayesian Neural Networks for Fluid Simulations , PDF: https://arxiv.org/pdf/2205.01222

NeuroFluid: Fluid Dynamics Grounding with Particle-Driven Neural Radiance Fields , PDF: https://arxiv.org/pdf/2203.01762.pdf

Deep neural networks to correct sub-precision errors in CFD , PDF: https://arxiv.org/pdf/2202.04233

Deep learning fluid flow reconstruction around arbitrary two-dimensional objects from sparse sensors using conformal mappings , PDF: https://arxiv.org/pdf/2202.03798.pdf

Predicting Physics in Mesh-reduced Space with Temporal Attention , PDF: https://arxiv.org/pdf/2201.09113.pdf

Inferring Turbulent Parameters via Machine Learning , PDF: https://arxiv.org/pdf/2201.00732

Learned Coarse Models for Efficient Turbulence Simulation , PDF: https://arxiv.org/pdf/2112.15275.pdf

Deep Learning for Stability Analysis of a Freely Vibrating Sphere at Moderate Reynolds Number , PDF: https://arxiv.org/pdf/2112.09858.pdf

Predicting High-Resolution Turbulence Details in Space and Time , PDF: http://geometry.caltech.edu/pubs/BWDL21.pdf

Assessments of model-form uncertainty using Gaussian stochastic weight averaging for fluid-flow regression , PDF: https://arxiv.org/pdf/2109.08248.pdf

Reconstructing High-resolution Turbulent Flows Using Physics-Guided Neural Networks , PDF: https://arxiv.org/pdf/2109.03327

Towards extraction of orthogonal and parsimonious non-linear modes from turbulent flows , PDF: https://arxiv.org/pdf/2109.01514.pdf

SURFNet: Super-resolution of Turbulent Flows with Transfer Learning using Small Datasets , PDF: https://arxiv.org/pdf/2108.07667.pdf

Deep Learning for Reduced Order Modelling and Efficient Temporal Evolution of Fluid Simulations , PDF: https://arxiv.org/pdf/2107.04556.pdf

Learning Incompressible Fluid Dynamics from Scratch - Towards Fast, Differentiable Fluid Models that Generalize , PDF: https://cg.cs.uni-bonn.de/aigaion2root/attachments/Paper.pdf

Scientific multi-agent reinforcement learning for wall-models of turbulent flows , PDF: https://arxiv.org/pdf/2106.11144.pdf

Simulating Continuum Mechanics with Multi-Scale Graph Neural Networks , PDF: https://arxiv.org/pdf/2106.04900.pdf

Embedded training of neural-network sub-grid-scale turbulence models , PDF: https://arxiv.org/pdf/2105.01030.pdf

Optimal control of point-to-point navigation in turbulent time dependent flows using Reinforcement Learning , PDF: https://arxiv.org/pdf/2103.00329.pdf

Machine learning accelerated computational fluid dynamics , PDF: https://arxiv.org/pdf/2102.01010.pdf

Neural Particle Image Velocimetry , PDF: https://arxiv.org/pdf/2101.11950.pdf

A turbulent eddy-viscosity surrogate modeling framework for Reynolds-Averaged Navier-Stokes simulations , Project+Code: https://www.sciencedirect.com/science/article/abs/pii/S0045793020303479

Super-resolution and denoising of fluid flow using physics-informed convolutional neural networks without high-resolution labels , PDF: https://arxiv.org/pdf/2011.02364.pdf

A Point-Cloud Deep Learning Framework for Prediction of Fluid Flow Fields on Irregular Geometries , PDF: https://arxiv.org/pdf/2010.09469

Learning Mesh-Based Simulations with Graph Networks , PDF: https://arxiv.org/pdf/2010.03409

Using Machine Learning to Augment Coarse-Grid Computational Fluid Dynamics Simulations , PDF: https://arxiv.org/pdf/2010.00072

Learning to swim in potential flow , PDF: https://arxiv.org/pdf/2009.14280

A neural network multigrid solver for the Navier-Stokes equations , PDF: https://arxiv.org/pdf/2008.11520.pdf

Enhanced data efficiency using deep neural networks and Gaussian processes for aerodynamic design optimization , PDF: https://arxiv.org/pdf/2008.06731

Learned discretizations for passive scalar advection in a 2-D turbulent flow , PDF: https://arxiv.org/pdf/2004.05477

PhyGeoNet: Physics-Informed Geometry-Adaptive Convolutional Neural Networks for Solving Parameterized Steady-State PDEs on Irregular Domain , PDF: https://arxiv.org/pdf/2004.13145

Combining Differentiable PDE Solvers and Graph Neural Networks for Fluid Flow Prediction , PDF: https://proceedings.icml.cc/static/paper_files/icml/2020/6414-Paper.pdf

CFDNet: A deep learning-based accelerator for fluid simulations , PDF: https://arxiv.org/pdf/2005.04485

The neural particle method--an updated Lagrangian physics informed neural network for computational fluid dynamics , PDF: https://arxiv.org/pdf/2003.10208

Controlling Rayleigh-Benard convection via Reinforcement Learning , PDF: https://arxiv.org/pdf/2003.14358

Embedding Hard Physical Constraints in Neural Network Coarse-Graining of 3D Turbulence , PDF: https://arxiv.org/pdf/2002.00021

Learning to Simulate Complex Physics with Graph Networks , PDF: https://arxiv.org/pdf/2002.09405

DPM: A deep learning PDE augmentation method (with application to large-eddy simulation) , PDF: https://arxiv.org/pdf/1911.09145

Towards Physics-informed Deep Learning for Turbulent Flow Prediction , PDF: https://arxiv.org/pdf/1911.08655

Dynamic Upsampling of Smoke through Dictionary-based Learning , PDF: https://arxiv.org/pdf/1910.09166

Deep unsupervised learning of turbulence for inflow generation at various Reynolds numbers , PDF: https://arxiv.org/pdf/1908.10515

DeepFlow: History Matching in the Space of Deep Generative Models , PDF: https://arxiv.org/pdf/1905.05749

Deep learning observables in computational fluid dynamics , PDF: https://arxiv.org/pdf/1903.03040

Compressed convolutional LSTM: An efficient deep learning framework to model high fidelity 3D turbulence , PDF: https://arxiv.org/pdf/1903.00033

Physics-constrained deep learning for high-dimensional surrogate modeling and uncertainty quantification without labeled data , PDF: https://arxiv.org/pdf/1901.06314.pdf

Deep neural networks for data-driven LES closure models , PDF: https://www.sciencedirect.com/science/article/pii/S0021999119306151

Computing interface curvature from volume fractions: A machine learning approach , PDF: https://www.sciencedirect.com/science/article/abs/pii/S0045793019302282

Machine learning the kinematics of spherical particles in fluid flows , PDF: https://sandlab.mit.edu/wp-content/uploads/18_JFM.pdf

Deep Neural Networks for Data-Driven Turbulence Models , PDF: https://export.arxiv.org/pdf/1806.04482

Deep Dynamical Modeling and Control of Unsteady Fluid Flows , PDF: http://papers.nips.cc/paper/8138-deep-dynamical-modeling-and-control-of-unsteady-fluid-flows

Learning Particle Dynamics for Manipulating Rigid Bodies, Deformable Objects, and Fluids , Project+Code: http://dpi.csail.mit.edu

Application of Convolutional Neural Network to Predict Airfoil Lift Coefficient , PDF: https://arxiv.org/pdf/1712.10082

Prediction of laminar vortex shedding over a cylinder using deep learning , PDF: https://arxiv.org/pdf/1712.07854

Lat-Net: Compressing Lattice Boltzmann Flow Simulations using Deep Neural Networks , PDF: https://arxiv.org/pdf/1705.09036

Reasoning About Liquids via Closed-Loop Simulation , PDF: https://arxiv.org/pdf/1703.01656

Prediction model of velocity field around circular cylinder over various Reynolds numbers by fusion convolutional neural networks based on pressure on the cylinder , PDF: https://doi.org/10.1063/1.5024595

Accelerating Eulerian Fluid Simulation With Convolutional Networks , Project+Code: https://cims.nyu.edu/~schlacht/CNNFluids.htm

Reynolds averaged turbulence modelling using deep neural networks with embedded invariance , PDF: https://www.labxing.com/files/lab_publications/2259-1524535041-QiPuSd6O.pdf

Image divider for general PDE section

Additional Links for General PDEs

Differentiable programming across the PDE and Machine Learning barrier , PDF: https://arxiv.org/abs/2409.06085

Zero-shot forecasting of chaotic systems , PDF: https://arxiv.org/pdf/2409.15771

Generative Learning for Forecasting the Dynamics of Complex Systems , PDF: https://arxiv.org/pdf/2402.17157

Micro-Macro Consistency in Multiscale Modeling: Score-Based Model Assisted Sampling of Fast/Slow Dynamical Systems , PDF: https://arxiv.org/pdf/2312.05715

Machine Learning for Partial Differential Equations , PDF: https://arxiv.org/pdf/2303.17078.pdf

Learning to Accelerate Partial Differential Equations via Latent Global Evolution , Project: http://snap.stanford.edu/le_pde/

Implicit Neural Spatial Representations for Time-dependent PDEs , PDF: https://proceedings.mlr.press/v202/chen23af/chen23af.pdf

Noise-aware physics-informed machine learning for robust PDE discovery , PDF: https://iopscience.iop.org/article/10.1088/2632-2153/acb1f0/pdf

Learning from Predictions: Fusing Training and Autoregressive Inference for Long-Term Spatiotemporal Forecasts , PDF: https://arxiv.org/pdf/2302.11101.pdf

Evolve Smoothly, Fit Consistently: Learning Smooth Latent Dynamics For Advection-Dominated Systems , PDF: https://arxiv.org/pdf/2301.10391

Continuous PDE dynamics forecasting with implicit neural representations , PDF: https://arxiv.org/pdf/2209.14855

Discovery of partial differential equations from highly noisy and sparse data with physics-informed information criterion , PDF: https://arxiv.org/pdf/2208.03322

Discovering nonlinear pde from scarce data with physics encoded learning , PDF: https://arxiv.org/pdf/2201.12354.pdf

CROM: Continuous Reduced-Order Modeling of PDEs Using Implicit Neural Representations , PDF: https://arxiv.org/pdf/2206.02607.pdf

Learning to Solve PDE-constrained Inverse Problems with Graph Networks , Project: https://cyanzhao42.github.io/LearnInverseProblem

CAN-PINN: A Fast Physics-Informed Neural Network Based on Coupled-Automatic-Numerical Differentiation Method , PDF: https://arxiv.org/pdf/2110.15832

Physics-Aware Downsampling with Deep Learning for Scalable Flood Modeling , PDF: https://arxiv.org/pdf/2106.07218v1.pdf

Learning Functional Priors and Posteriors from Data and Physics , PDF: https://arxiv.org/pdf/2106.05863.pdf

Accelerating Neural ODEs Using Model Order Reduction , PDF: https://arxiv.org/pdf/2105.14070

Adversarial Multi-task Learning Enhanced Physics-informed Neural Networks for Solving Partial Differential Equations , PDF: https://arxiv.org/pdf/2104.14320

gradSim: Differentiable simulation for system identification and visuomotor control , Project: https://gradsim.github.io

Physics-aware, probabilistic model order reduction with guaranteed stability , PDF: https://arxiv.org/pdf/2101.05834

Learning Poisson systems and trajectories of autonomous systems via Poisson neural networks , PDF: https://arxiv.org/pdf/2012.03133.pdf

Aphynity: Augmenting physical models with deep networks for complex dynamics forecasting , PDF: https://arxiv.org/pdf/2010.04456.pdf

Hierarchical Deep Learning of Multiscale Differential Equation Time-Steppers , PDF: https://arxiv.org/pdf/2008.09768

Learning Compositional Koopman Operators for Model-Based Control , Project: http://koopman.csail.mit.edu

Universal Differential Equations for Scientific Machine Learning , PDF: https://arxiv.org/pdf/2001.04385.pdf

Understanding and mitigating gradient pathologies in physics-informed neural networks , PDF: https://arxiv.org/pdf/2001.04536

Variational Physics-Informed Neural Networks For Solving Partial Differential Equations , PDF: https://arxiv.org/pdf/1912.00873

Poisson CNN: Convolutional Neural Networks for the Solution of the Poisson Equation with Varying Meshes and Dirichlet Boundary Conditions , PDF: https://arxiv.org/pdf/1910.08613

IDENT: Identifying Differential Equations with Numerical Time evolution , PDF: https://arxiv.org/pdf/1904.03538

PDE-Net 2.0: Learning PDEs from Data with A Numeric-Symbolic Hybrid Deep Network , PDF: https://arxiv.org/pdf/1812.04426

Data-driven discretization: a method for systematic coarse graining of partial differential equations , PDF: https://arxiv.org/pdf/1808.04930

Solving high-dimensional partial differential equations using deep learning , PDF: https://www.pnas.org/content/115/34/8505.full.pdf

Neural Ordinary Differential Equations , PDF: https://arxiv.org/pdf/1806.07366

Deep Learning the Physics of Transport Phenomena , PDF: https://arxiv.org/pdf/1709.02432

DGM: A deep learning algorithm for solving partial differential equations , PDF: https://arxiv.org/pdf/1708.07469

Hidden Physics Models: Machine Learning of Nonlinear Partial Differential Equations , PDF: https://arxiv.org/pdf/1708.00588

Data-assisted reduced-order modeling of extreme events in complex dynamical systems , Project+Code: https://github.com/zhong1wan/data-assisted

PDE-Net: Learning PDEs from Data , Project+Code: https://github.com/ZichaoLong/PDE-Net

Learning Deep Neural Network Representations for Koopman Operators of Nonlinear Dynamical Systems , PDF: https://arxiv.org/pdf/1708.06850

Neural-network-based approximations for solving partial differential equations , DOI: https://doi.org/10.1002/cnm.1640100303

Additional Links for Other Physics Problems and Physics-related Problems

Advancing Generalization in PINNs through Latent-Space Representations , PDF: https://arxiv.org/pdf/2411.19125

Text2PDE: Latent Diffusion Models for Accessible Physics Simulation , PDF: https://arxiv.org/abs/2410.01137

Active Learning for Neural PDE Solvers , PDF: https://arxiv.org/pdf/2408.01536

Physics-embedded Fourier Neural Network for Partial Differential Equations ,
PDF: https://arxiv.org/pdf/2407.11158

Accelerating Legacy Numerical Solvers by Non-intrusive Gradient-based Meta-solving , PDF: https://arxiv.org/pdf/2405.02952

Vectorized Conditional Neural Fields: A Framework for Solving Time-dependent Parametric Partial Differential Equations , Project: https://jhagnberger.github.io/vectorized-conditional-neural-field/

UM2N: Towards Universal Mesh Movement Networks , PDF: https://arxiv.org/pdf/2407.00382

Physics-Aware Neural Implicit Solvers for multiscale, parametric PDEs with applications in heterogeneous media ,
PDF: https://arxiv.org/pdf/2405.19019

Hybrid Modeling Design Patterns , PDF: https://arxiv.org/pdf/2401.00033

ClimODE: Climate Forecasting With Physics-informed Neural ODEs , PDF: https://openreview.net/pdf?id=xuY33XhEGR

Pretraining Codomain Attention Neural Operators for Solving Multiphysics PDEs , PDF: https://arxiv.org/pdf/2403.12553

Investigation of the generalization capability of a generative adversarial network for large eddy simulation of turbulent premixed reacting flows , PDF: https://www.sciencedirect.com/science/article/pii/S1540748922002851

Optimal Power Flow in Highly Renewable Power System Based on Attention Neural Networks , PDF: https://arxiv.org/pdf/2311.13949

Neural General Circulation Models , PDF: https://arxiv.org/pdf/2311.07222

A neural-preconditioned poisson solver for mixed dirichlet and neumann boundary conditions , PDF: https://arxiv.org/pdf/2310.00177.pdf

Neural stream functions , PDF: https://arxiv.org/pdf/2307.08142.pdf

Stabilized Neural Differential Equations for Learning Constrained Dynamics , PDF: https://arxiv.org/pdf/2306.09739

Combining Slow and Fast: Complementary Filtering for Dynamics Learning , PDF: https://arxiv.org/pdf/2302.13754.pdf

PDEBench: An Extensive Benchmark for Scientific Machine Learning , Project: https://github.com/pdebench/PDEBench

Efficient Learning of Mesh-Based Physical Simulation with Bi-Stride Multi-Scale Graph Neural Network , PDF: https://arxiv.org/pdf/2210.02573.pdf

Scalable Bayesian Uncertainty Quantification for Neural Network Potentials: Promise and Pitfalls , PDF: https://arxiv.org/pdf/2212.07959

Breaking Bad: A Dataset for Geometric Fracture and Reassembly , Project: https://arxiv.org/pdf/2210.11463

Probabilistic forecasts of extreme heatwaves using convolutional neural networks in a regime of lack of data , PDF: https://arxiv.org/pdf/2208.00971

Equiformer: Equivariant Graph Attention Transformer for 3D Atomistic Graphs , PDF: https://arxiv.org/pdf/2206.11990

Symplectically Integrated Symbolic Regression of Hamiltonian Dynamical Systems , PDF: https://arxiv.org/pdf/2209.01521.pdf

Contact Points Discovery for Soft-Body Manipulations with Differentiable Physics , PDF: https://arxiv.org/pdf/2205.02835.pdf

Message Passing Neural PDE Solvers , PDF: https://arxiv.org/pdf/2202.03376

A Survey on Machine Learning Approaches for Modelling Intuitive Physics , PDF: https://arxiv.org/pdf/2202.06481

Fine-grained differentiable physics: a yarn-level model for fabrics , PDF: https://arxiv.org/pdf/2202.00504

Accurately Solving Rod Dynamics with Graph Learning , PDF: http://computationalsciences.org/publications/shao-2021-physical-systems-graph-learning/shao-2021-physical-systems-graph-learning.pdf

Constraint-based graph network simulator , PDF: https://arxiv.org/pdf/2112.09161

Differentiable Simulation of Soft Multi-body Systems , PDF: https://arxiv.org/pdf/2205.01758

Learning Material Parameters and Hydrodynamics of Soft Robotic Fish via Differentiable Simulation , PDF: https://arxiv.org/pdf/2109.14855

Model Reduction for the Material Point Method via Learning the Deformation map and its Spatial-temporal Gradients , Project: https://peterchencyc.com/projects/rom4mpm/

PhysGNN: A Physics–Driven Graph Neural Network Based Model for Predicting Soft Tissue Deformation in Image–Guided Neurosurgery , PDF: https://arxiv.org/pdf/2109.04352.pdf

Deep learning for surrogate modelling of 2D mantle convection , PDF: https://arxiv.org/pdf/2108.10105

An Extensible Benchmark Suite for Learning to Simulate Physical Systems , PDF: https://arxiv.org/pdf/2108.07799

Turbulent field fluctuations in gyrokinetic and fluid plasmas , PDF: https://arxiv.org/pdf/2107.09744.pdf

Robust Value Iteration for Continuous Control Tasks , PDF: https://arxiv.org/pdf/2105.12189

Fast and Feature-Complete Differentiable Physics for Articulated Rigid Bodies with Contact , PDF: https://arxiv.org/pdf/2103.16021

High-order Differentiable Autoencoder for Nonlinear Model Reduction , PDF: https://arxiv.org/pdf/2102.11026.pdf

Modeling of the nonlinear flame response of a Bunsen-type flame via multi-layer perceptron , Paper: https://www.sciencedirect.com/science/article/pii/S1540748920305666

Deluca – A Differentiable Control Library: Environments, Methods, and Benchmarking , PDF: https://montrealrobotics.ca/diffcvgp/assets/papers/1.pdf

Deep Energy-based Modeling of Discrete-Time Physics , PDF: https://proceedings.neurips.cc/paper/2020/file/98b418276d571e623651fc1d471c7811-Paper.pdf

NeuralSim: Augmenting Differentiable Simulators with Neural Networks , PDF: https://arxiv.org/pdf/2011.04217.pdf

Fourier Neural Operator for Parametric Partial Differential Equations , PDF: https://arxiv.org/pdf/2010.08895.pdf

Learning Composable Energy Surrogates for PDE Order Reduction , PDF: https://arxiv.org/pdf/2005.06549.pdf

Transformers for Modeling Physical Systems , PDF: https://arxiv.org/pdf/2010.03957

Reinforcement Learning for Molecular Design Guided by Quantum Mechanics , PDF: https://proceedings.icml.cc/static/paper_files/icml/2020/1323-Paper.pdf

Scalable Differentiable Physics for Learning and Control , PDF: https://proceedings.icml.cc/static/paper_files/icml/2020/15-Paper.pdf

Cloth in the Wind: A Case Study of Physical Measurement through Simulation , PDF: https://arxiv.org/pdf/2003.05065

Learning to Slide Unknown Objects with Differentiable Physics Simulations , PDF: https://arxiv.org/pdf/2005.05456

Physics-aware Difference Graph Networks for Sparsely-Observed Dynamics , Project: https://github.com/USC-Melady/ICLR2020-PADGN

Differentiable Molecular Simulations for Control and Learning , PDF: https://arxiv.org/pdf/2003.00868

Incorporating Symmetry into Deep Dynamics Models for Improved Generalization , PDF: https://arxiv.org/pdf/2002.03061

Learning to Measure the Static Friction Coefficient in Cloth Contact , PDF: https://hal.inria.fr/hal-02511646

Learning to Simulate Complex Physics with Graph Networks , PDF: https://arxiv.org/pdf/2002.09405

Hamiltonian Neural Networks , PDF: http://papers.nips.cc/paper/9672-hamiltonian-neural-networks.pdf

Interactive Differentiable Simulation , PDF: https://arxiv.org/pdf/1905.10706

DiffTaichi: Differentiable Programming for Physical Simulation , PDF: https://arxiv.org/pdf/1910.00935

Physics-Constrained Deep Learning for High-dimensional Surrogate Modeling and Uncertainty Quantification without Labeled Data , PDF: https://arxiv.org/pdf/1901.06314

COPHY: Counterfactual Learning of Physical Dynamics , Project: https://github.com/fabienbaradel/cophy

Modeling Expectation Violation in Intuitive Physics with Coarse Probabilistic Object Representations , Project: http://physadept.csail.mit.edu

End-to-End Differentiable Physics for Learning and Control , Project+Code: https://github.com/locuslab/lcp-physics

Stochastic seismic waveform inversion using generative adversarial networks as a geological prior , PDF: https://arxiv.org/pdf/1806.03720

Learning to Optimize Multigrid PDE Solvers , PDF: http://proceedings.mlr.press/v97/greenfeld19a/greenfeld19a.pdf

Latent-space Dynamics for Reduced Deformable Simulation , Project+Code: http://www.dgp.toronto.edu/projects/latent-space-dynamics/

Learning-Based Animation of Clothing for Virtual Try-On , PDF: http://www.gmrv.es/Publications/2019/SOC19/

Deep Lagrangian Networks: Using Physics as Model Prior for Deep Learning , PDF: https://openreview.net/pdf?id=BklHpjCqKm

Flexible Neural Representation for Physics Prediction , Project+Code: https://neuroailab.github.io/physics/

Robust Reference Frame Extraction from Unsteady 2D Vector Fields with Convolutional Neural Networks , PDF: https://arxiv.org/pdf/1903.10255

Physics-as-Inverse-Graphics: Joint Unsupervised Learning of Objects and Physics from Video , PDF: https://arxiv.org/pdf/1905.11169

Unsupervised Intuitive Physics from Past Experiences , PDF: https://arxiv.org/pdf/1905.10793

Reasoning About Physical Interactions with Object-Oriented Prediction and Planning , PDF: https://arxiv.org/pdf/1812.10972

Neural Material: Learning Elastic Constitutive Material and Damping Models from Sparse Data , PDF: https://arxiv.org/pdf/1808.04931

Discovering physical concepts with neural networks , PDF: https://arxiv.org/pdf/1807.10300

Fluid directed rigid body control using deep reinforcement learning , Project: http://gamma.cs.unc.edu/DRL_FluidRigid/

DeepMimic, Example-Guided Deep Reinforcement Learning of Physics-Based Character Skills , PDF: https://arxiv.org/pdf/1804.02717

Unsupervised Intuitive Physics from Visual Observations , PDF: https://arxiv.org/pdf/1805.05086

Graph networks as learnable physics engines for inference and control , PDF: https://arxiv.org/pdf/1806.01242

DeepWarp: DNN-based Nonlinear Deformation , PDF: https://arxiv.org/pdf/1803.09109

A proposal on machine learning via dynamical systems , Journal: https://link.springer.com/article/10.1007/s40304-017-0103-z

Interaction Networks for Learning about Objects, Relations and Physics , PDF: https://arxiv.org/pdf/1612.00222

Surveys and Overview Articles

Physics-Guided Deep Learning for Dynamical Systems: A Survey , PDF: https://arxiv.org/pdf/2107.01272

Integrating Physics-Based Modeling with Machine Learning: A Survey , PDF: https://arxiv.org/pdf/2003.04919

Integrating Machine Learning with Physics-Based Modeling , PDF: https://arxiv.org/pdf/2006.02619

A review on Deep Reinforcement Learning for Fluid Mechanics , PDF: https://arxiv.org/pdf/1908.04127

Machine Learning for Fluid Mechanics , PDF: https://arxiv.org/pdf/1905.11075

Simulation and Deep Learning Frameworks

PhiFlow: https://github.com/tum-pbs/phiflow

Diff-Taichi: https://github.com/yuanming-hu/difftaichi

Jax-Md: https://github.com/google/jax-md

TensorFlow-Foam: https://github.com/argonne-lcf/TensorFlowFoam

Julia-Sciml: https://sciml.ai

GradSim: https://gradsim.github.io

Jax-Cfd: https://github.com/google/jax-cfd

Jax-Fluids: https://github.com/tumaer/JAXFLUIDS

Concluding Remarks

Physics-based deep learning is a very dynamic field. Please let us know if we've overlooked papers that you think should be included by sending a mail to i15ge at cs.tum.de, and feel free to check out our homepage at https://ge.in.tum.de/.

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Links to works on deep learning algorithms for physics problems, TUM-I15 and beyond

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