Improving physics-informed DeepONets with hard constraints
This addresses a limitation in physics-informed deep learning for solving differential equations, though it appears incremental as it builds on existing DeepONet frameworks.
The paper tackled the problem of physics-informed neural networks needing to learn initial/boundary conditions by proposing a method that enforces these conditions exactly, ensuring continuity in time-stepping solutions.
Current physics-informed (standard or deep operator) neural networks still rely on accurately learning the initial and/or boundary conditions of the system of differential equations they are solving. In contrast, standard numerical methods involve such conditions in computations without needing to learn them. In this study, we propose to improve current physics-informed deep learning strategies such that initial and/or boundary conditions do not need to be learned and are represented exactly in the predicted solution. Moreover, this method guarantees that when a deep operator network is applied multiple times to time-step a solution of an initial value problem, the resulting function is at least continuous.