DSGNAR optimization framework for PINNs reaches relative L2 errors of 3e-16 in double precision and improves prior results by 5-8 orders of magnitude on Burgers' and high-dimensional Poisson problems while remaining faster.
TINNs: Time-Induced Neural Networks for Solving Time-Dependent PDEs
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abstract
Physics-informed neural networks (PINNs) solve time-dependent partial differential equations (PDEs) by learning a mesh-free, differentiable solution that can be evaluated anywhere in space and time. However, standard space-time PINNs take time as an input but reuse a single network with shared weights across all times, forcing the same features to represent markedly different dynamics. This coupling degrades error performance and can destabilize training when enforcing PDE, boundary, and initial constraints jointly. We propose Time-Induced Neural Networks (TINNs), a novel architecture that parameterizes the network weights as a learned function of time, allowing the effective spatial representation to evolve over time while maintaining shared structure. The resulting formulation naturally yields a nonlinear least-squares problem, which we optimize efficiently using a Levenberg-Marquardt method. Experiments on various time-dependent PDEs show up to 4 times improved relative error and 10 times faster convergence compared to PINNs and strong baselines.
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cs.LG 1years
2026 1verdicts
UNVERDICTED 1representative citing papers
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An Optimisation Framework for the Well-Conditioned Training of Physics-Informed Neural Networks
DSGNAR optimization framework for PINNs reaches relative L2 errors of 3e-16 in double precision and improves prior results by 5-8 orders of magnitude on Burgers' and high-dimensional Poisson problems while remaining faster.