mlsanityData to 13 Oct 2026

PI-VAE: Physics-Informed Variational Auto-Encoder for stochastic differential equations

arXiv 2203.11363 ↗First posted 21 Mar 2022stat.ML cs.LGcited by 21

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Abstract (arXiv)

We propose a new class of physics-informed neural networks, called physics-informed Variational Autoencoder (PI-VAE), to solve stochastic differential equations (SDEs) or inverse problems involving SDEs. In these problems the governing equations are known but only a limited number of measurements of system parameters are available. PI-VAE consists of a variational autoencoder (VAE), which generates samples of system variables and parameters. This generative model is integrated with the governing equations. In this integration, the derivatives of VAE outputs are readily calculated using automatic differentiation, and used in the physics-based loss term. In this work, the loss function is chosen to be the Maximum Mean Discrepancy (MMD) for improved performance, and neural network parameters are updated iteratively using the stochastic gradient descent algorithm. We first test the proposed method on approximating stochastic processes. Then we study three types of problems related to SDEs: forward and inverse problems together with mixed problems where system parameters and solutions are simultaneously calculated. The satisfactory accuracy and efficiency of the proposed method are numerically demonstrated in comparison with physics-informed generative adversarial network (PI-WGAN).

Key facts. Cited by 21 papers in the map (data through 13 Oct 2026). Builds on 19 of its 40 references that are in the map. First posted on arXiv 21 Mar 2022.

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19 of 40 references.

References · 19

  1. 2022Generative Adversarial Networkscited by 5,614
  2. 2013Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distancescited by 2,295
  3. 2017Improved Training of Wasserstein GANscited by 2,226
  4. 2021Learning the solution operator of parametric partial differential equations with physics-informed DeepOnetscited by 538
  5. 2017Wasserstein Auto-Encoderscited by 372
  6. 2017Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equationscited by 368
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  8. 2017Deep learning-based numerical methods for high-dimensional parabolic partial differential equations and backward stochastic differential equationscited by 188
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  10. 2018Quantifying total uncertainty in physics-informed neural networks for solving forward and inverse stochastic problemscited by 147
  11. 2018Physics-Informed Generative Adversarial Networks for Stochastic Differential Equationscited by 135
  12. 2018Adversarial Uncertainty Quantification in Physics-Informed Neural Networkscited by 120
7 more
  1. 2016Generative Models and Model Criticism via Optimized Maximum Mean Discrepancycited by 99
  2. 2020Sparse Polynomial Chaos Expansions: Literature Survey and Benchmarkcited by 44
  3. 2018A Deep Neural Network Surrogate for High-Dimensional Random Partial Differential Equationscited by 23
  4. 2021PID-GAN: A GAN Framework based on a Physics-informed Discriminator for Uncertainty Quantification with Physicscited by 21
  5. 2019Highly-scalable, physics-informed GANs for learning solutions of stochastic PDEscited by 11
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Cited by year (2026 to 13 Oct)

Citing papers per year: 2022: 1; 2023: 7; 2024: 2; 2025: 7; 2026: 4.

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  1. 2023L-HYDRA: Multi-Head Physics-Informed Neural Networkscited by 29
  2. 2022Fully probabilistic deep models for forward and inverse problems in parametric PDEscited by 19
  3. 2025Four Principles for Physically Interpretable World Modelscited by 10
  4. 2023Random Grid Neural Processes for Parametric Partial Differential Equationscited by 8
  5. 2023HyperSINDy: Deep Generative Modeling of Nonlinear Stochastic Governing Equationscited by 8
  6. 2025Geometry-Informed Neural Operator Transformercited by 8
  7. 2023InVAErt networks: a data-driven framework for model synthesis and identifiability analysiscited by 6
  8. 2023PI-VEGAN: Physics Informed Variational Embedding Generative Adversarial Networks for Stochastic Differential Equationscited by 4
  9. 2024A Primer on Variational Inference for Physics-Informed Deep Generative Modellingcited by 3
  10. 2024Physically Interpretable World Models via Weakly Supervised Representation Learningcited by 3
  11. 2025SPIEDiff: robust learning of long-time macroscopic dynamics from short-time particle simulations with quantified epistemic uncertaintycited by 2
  12. 2025Adversarial Disentanglement by Backpropagation with Physics-Informed Variational Autoencodercited by 2
9 more
  1. 2025Variational Rank Reduction Autoencoders for Generative Thermal Designcited by 1
  2. 2023PartitionVAE -- a human-interpretable VAEcited by 0
  3. 2023Physics informed Neural Networks applied to the description of wave-particle resonance in kinetic simulations of fusion plasmascited by 0
  4. 2025Scalable physics-informed deep generative model for solving forward and inverse stochastic differential equationscited by 0
  5. 2025Physically-Grounded Goal Imagination: Physics-Informed Variational Autoencoder for Self-Supervised Reinforcement Learningcited by 0
  6. 2026High-Fidelity Modeling of Stochastic Chemical Dynamics on Complex Manifolds: A Multi-Scale SIREN-PINN Framework for the Curvature-Perturbed Ginzburg-Landau Equationcited by 0
  7. 2026Target-Aware Linear Regression Under Distribution Shiftcited by 0
  8. 2026Structure-preserving uncertainty quantification for GENERIC dynamicscited by 0
  9. 2026CEENs: Causality-enforced evolutional networks for solving time-dependent partial differential equationscited by 0