PI-VAE: Physics-Informed Variational Auto-Encoder for stochastic differential equations
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).
Code (1)
Tasks
Generative Adversarial NetworkSimilar Papers 제목 키워드 기반
PI-VEGAN: Physics Informed Variational Embedding Generative Adversarial Networks for Stochastic Differential Equations
We present a new category of physics-informed neural networks called physics informed variational embedding generative adversarial network (PI-VEGAN), that effectively tackles the forward, inverse, and mixed problems of …
Generative Adversarial NetworkPhysically-Grounded Goal Imagination: Physics-Informed Variational Autoencoder for Self-Supervised Reinforcement Learning
Self-supervised goal-conditioned reinforcement learning enables robots to autonomously acquire diverse skills without human supervision. However, a central challenge is the goal setting problem: robots must propose feasi…
Reinforcement LearningAdversarial Disentanglement by Backpropagation with Physics-Informed Variational Autoencoder
Inference and prediction under partial knowledge of a physical system is challenging, particularly when multiple confounding sources influence the measured response. Explicitly accounting for these influences in physics-…
DisentanglementUncertainty-aware damage identification in short-span bridges via physics-informed variational autoencoder
Vibration-based damage identification in civil infrastructure is a challenging, ill-posed inverse problem due to measurement noise, sparse sensor arrays, and environmental variability. While deep learning is powerful for…
Physics-informed generative neural networks for RF propagation prediction with application to indoor body perception
Electromagnetic (EM) body models designed to predict Radio-Frequency (RF) propagation are time-consuming methods which prevent their adoption in strict real-time computational imaging problems, such as human body localiz…