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Physics-informed neural networks (PINNs) as a means of solving partialdifferential equations (PDE) have garnered much attention in the ComputationalScience and Engineering (CS&E) world. However, a recent topic of interest isexploring various training (i.e., optimization) challenges - in particular,arriving at poor local minima in the optimization landscape results in a PINNapproximation giving an inferior, and sometimes trivial, solution when solvingforward time-dependent PDEs with no data. This problem is also found in, and insome sense more difficult, with domain decomposition strategies such astemporal decomposition using XPINNs. We furnish examples and explanations fordifferent training challenges, their cause, and how they relate to informationpropagation and temporal decomposition. We then propose a newstacked-decomposition method that bridges the gap between time-marching PINNsand XPINNs. We also introduce significant computational speed-ups by usingtransfer learning concepts to initialize subnetworks in the domain and losstolerance-based propagation for the subdomains. Finally, we formulate a newtime-sweeping collocation point algorithm inspired by the previous PINNscausality literature, which our framework can still describe, and provides asignificant computational speed-up via reduced-cost collocation pointsegmentation. The proposed methods form our unified framework, which overcomestraining challenges in PINNs and XPINNs for time-dependent PDEs by respectingthe causality in multiple forms and improving scalability by limiting thecomputation required per optimization iteration. Finally, we provide numericalresults for these methods on baseline PDE problems for which unmodified PINNsand XPINNs struggle to train.

A unified scalable framework for causal sweeping strategies for Physics-Informed Neural Networks (PINNs) and their temporal decompositions