Physics-Informed Generator-Encoder Adversarial Networks with Latent Space Matching for Stochastic Differential Equations
This addresses challenges in solving stochastic differential equations for applications like physics and engineering, but appears incremental as it builds on prior physics-informed neural networks and adversarial frameworks.
The authors tackled forward, inverse, and mixed problems in stochastic differential equations with limited snapshot data by proposing Physics-Informed Generator-Encoder Adversarial Networks, achieving more accurate solutions compared to existing neural network solvers and mitigating training instability.
We propose a new class of physics-informed neural networks, called Physics-Informed Generator-Encoder Adversarial Networks, to effectively address the challenges posed by forward, inverse, and mixed problems in stochastic differential equations. In these scenarios, while the governing equations are known, the available data consist of only a limited set of snapshots for system parameters. Our model consists of two key components: the generator and the encoder, both updated alternately by gradient descent. In contrast to previous approaches of directly matching the approximated solutions with real snapshots, we employ an indirect matching that operates within the lower-dimensional latent feature space. This method circumvents challenges associated with high-dimensional inputs and complex data distributions, while yielding more accurate solutions compared to existing neural network solvers. In addition, the approach also mitigates the training instability issues encountered in previous adversarial frameworks in an efficient manner. Numerical results provide compelling evidence of the effectiveness of the proposed method in solving different types of stochastic differential equations.