TINNs: Time-Induced Neural Networks for Solving Time-Dependent PDEs

• URL: http://arxiv.org/abs/2601.20361v1
• Date: Wed, 28 Jan 2026 08:23:28 GMT
• Title: TINNs: Time-Induced Neural Networks for Solving Time-Dependent PDEs
• Authors: Chen-Yang Dai, Che-Chia Chang, Te-Sheng Lin, Ming-Chih Lai, Chieh-Hsin Lai,
• Abstract summary: Physics-informed neural networks (PINNs) solve time-dependent partial differential equations (PDEs)<n> 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.<n>We propose Time-Induced Neural Networks (TINNs), a novel architecture that parameterizes the network weights as a learned function of time.
• Score: 7.031010831953522
• License: http://creativecommons.org/licenses/by/4.0/
• 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 accuracy 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 accuracy and $10\times$ faster convergence compared to PINNs and strong baselines.

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