mlsanityData to 14 Oct 2026

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

arXiv 2601.20361 ↗First posted 28 Jan 2026cs.LG cs.NA math.NAcited by 3

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Abstract (arXiv)

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.

Key facts. Cited by 3 papers in the map (data through 14 Oct 2026). Builds on 11 of its 24 references that are in the map. First posted on arXiv 28 Jan 2026.

Builds on

11 of 24 references.

References · 11

  1. 2015Deep Residual Learning for Image Recognitioncited by 52,096
  2. 2020Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domainscited by 2,200
  3. 2022Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's nextcited by 608
  4. 2021Multi-Objective Loss Balancing for Physics-Informed Deep Learningcited by 87
  5. 2024PirateNets: Physics-informed Deep Learning with Residual Adaptive Networkscited by 72
  6. 2023Separable Physics-Informed Neural Networkscited by 66
  7. 2025Gradient Alignment in Physics-informed Neural Networks: A Second-Order Optimization Perspectivecited by 56
  8. 2023Improving physics-informed neural networks with meta-learned optimizationcited by 19
  9. 2022Auto-PINN: Understanding and Optimizing Physics-Informed Neural Architecturecited by 14
  10. 2024Fast training of accurate physics-informed neural networks without gradient descentcited by 8
  11. 2021Learning without Data: Physics-Informed Neural Networks for Fast Time-Domain Simulationcited by 7

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2026: 3.

3 papers.

  1. 2026An Optimisation Framework for the Well-Conditioned Training of Physics-Informed Neural Networkscited by 1
  2. 2026From Non-Convex Self-Concordant Regularization to Scalable Quasi-Newton Training of PINNscited by 0
  3. 2026Beyond Time Induction: Structured Conditional Neural Solvers for Parametric Stochastic-Volatility Pricingcited by 0