  Modeling unsteady, fast transient, and advection-dominated physics problems
is a pressing challenge for physics-aware deep learning (PADL). The physics of
complex systems is governed by large systems of partial differential equations
(PDEs) and ancillary constitutive models with nonlinear structures, as well as
evolving state fields exhibiting sharp gradients and rapidly deforming material
interfaces. Here, we investigate an inductive bias approach that is versatile
and generalizable to model generic nonlinear field evolution problems. Our
study focuses on the recent physics-aware recurrent convolutions (PARC), which
incorporates a differentiator-integrator architecture that inductively models
the spatiotemporal dynamics of generic physical systems. We extend the
capabilities of PARC to simulate unsteady, transient, and advection-dominant
systems. The extended model, referred to as PARCv2, is equipped with
differential operators to model advection-reaction-diffusion equations, as well
as a hybrid integral solver for stable, long-time predictions. PARCv2 is tested
on both standard benchmark problems in fluid dynamics, namely Burgers and
Navier-Stokes equations, and then applied to more complex shock-induced
reaction problems in energetic materials. We evaluate the behavior of PARCv2 in
comparison to other physics-informed and learning bias models and demonstrate
its potential to model unsteady and advection-dominant dynamics regimes.
