Physics-informed generator-encoder adversarial networks with latent space matching for stochastic differential equations

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 (SDEs). In these scenarios, while 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 that directly match approximated solutions with real snapshots, we employ an indirect matching operating within the lower-dimensional latent feature space. This method circumvents challenges associated with high-dimensional inputs and complex data distributions in solving SDEs. Numerical experiments indicate that, compared to existing deep learning solvers, our proposed approach not only demonstrates superior accuracy but also exhibits advantages in both computational efficiency and model complexity.