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Sub-Sequential Physics-Informed Learning with State Space Model
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Physics-Informed Neural Networks (PINNs) are a kind of deep-learning-based numerical solvers for partial differential equations (PDEs). Existing PINNs often suffer from failure modes of being unable to propagate patterns of initial conditions. We discover that these failure modes are caused by the simplicity bias of neural networks and the mismatch between PDE's continuity and PINN's discrete sampling. We reveal that the State Space Model (SSM) can be a continuous-discrete articulation allowing initial condition propagation, and that simplicity bias can be eliminated by aligning a sequence of moderate granularity. Accordingly, we propose PINNMamba, a novel framework that introduces sub-sequence modeling with SSM. Experimental results show that PINNMamba can reduce errors by up to 86.3\% compared with state-of-the-art architecture. Our code is available at https://github.com/miniHuiHui/PINNMamba.
Forward citations
Cited by 4 Pith papers
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Cosmo-SPINN: Fuzzy Dark Matter Simulations with Physics-Informed Generative Networks
Physics-informed generative U-Nets evolve and super-resolve fuzzy dark matter fields under Schrödinger–Poisson constraints with far less supervised data than pure data-driven baselines.
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SPINN: Advancing Cosmological Simulations of Fuzzy Dark Matter with Physics Informed Neural Networks
A physics-informed neural network (SPINN) solves the Schrödinger-Poisson equations for fuzzy dark matter collapse in 1D and 3D, matching a spectral solver on a sinusoidal test case.
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Neural Multiscale Decomposition for Solving The Nonlinear Klein-Gordon Equation with Time Oscillation
NeuralMD solves the oscillatory NKGE by training one network on the slow NLSW envelope and another on the remainder, but its model-selection step requires the exact solution as ground truth.
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PIANO: Physics Informed Autoregressive Network
PIANO makes physics-informed neural networks autoregressive, rolling out predictions conditioned on past states under physics constraints, and claims stable, accurate long-horizon PDE and weather forecasts.
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