A spectral PINN approach to unresolved-scale closure in multiscale dynamics

Pengyu Lai, Dewu Yang, Rui Wang, Jing Wang and Hui Xu

Chaos, Solitons & Fractals, 2026, vol. 210, issue P2

Abstract: Multiscale systems are difficult to simulate because predictive fidelity often depends on unresolved small-scale dynamics even when the dominant large-scale evolution is already available. We propose a spectral physics-informed neural network (Spectral PINN) approach in which the resolved large-scale trajectory is supplied as input and only the unresolved correction is reconstructed in coefficient space. This formulation makes the resolved/unresolved decomposition explicit and allows spatial operators to be enforced directly in spectral coordinates, so that the physics-informed loss acts on the target unresolved modes while alleviating the spectral-bias difficulty encountered when standard PINNs are trained on the full field in physical space. We assess the approach on the one-dimensional Kuramoto–Sivashinsky equation and the two- and three-dimensional Navier–Stokes equations. Across these benchmarks, the method accurately recovers the unresolved-scale dynamics and remains effective even when the unresolved state is high dimensional. Additional studies on decomposition sensitivity, proper orthogonal decomposition (POD) coordinates, a finite-interval modified KS benchmark with homogeneous Dirichlet and Neumann boundary conditions, noisy resolved inputs, and uncertain unresolved initial conditions further clarify the method’s operating regime, basis dependence, and practical scope. Overall, the results show that learning only the unresolved component provides an effective and physically structured route to unresolved-scale closure in multiscale dynamics, and points to a promising direction for data-assisted multiscale simulation in which coarse large-scale descriptions are coupled with learned small-scale closure.

Keywords: Multiscale simulation; Physics-informed neural network; Large-scale dynamics; Small-scale dynamics (search for similar items in EconPapers)
Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:210:y:2026:i:p2:s0960077926008209

DOI: 10.1016/j.chaos.2026.118679

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