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

arXiv: https://arxiv.org/abs/2601.20361 · HTML: https://mlsanity.com/paper/2601.20361/

## 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 (most cited first, 11 of 11)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's next](https://mlsanity.com/paper/2201.05624/) (2022)
- [Multi-Objective Loss Balancing for Physics-Informed Deep Learning](https://mlsanity.com/paper/2110.09813/) (2021)
- [PirateNets: Physics-informed Deep Learning with Residual Adaptive Networks](https://mlsanity.com/paper/2402.00326/) (2024)
- [Separable Physics-Informed Neural Networks](https://mlsanity.com/paper/2306.15969/) (2023)
- [Gradient Alignment in Physics-informed Neural Networks: A Second-Order Optimization Perspective](https://mlsanity.com/paper/2502.00604/) (2025)
- [Improving physics-informed neural networks with meta-learned optimization](https://mlsanity.com/paper/2303.07127/) (2023)
- [Auto-PINN: Understanding and Optimizing Physics-Informed Neural Architecture](https://mlsanity.com/paper/2205.13748/) (2022)
- [Fast training of accurate physics-informed neural networks without gradient descent](https://mlsanity.com/paper/2405.20836/) (2024)
- [Learning without Data: Physics-Informed Neural Networks for Fast Time-Domain Simulation](https://mlsanity.com/paper/2106.15987/) (2021)

## Built on by (most cited first, 3 of 3)

- [An Optimisation Framework for the Well-Conditioned Training of Physics-Informed Neural Networks](https://mlsanity.com/paper/2607.02194/) (2026)
- [From Non-Convex Self-Concordant Regularization to Scalable Quasi-Newton Training of PINNs](https://mlsanity.com/paper/2608.04206/) (2026)
- [Beyond Time Induction: Structured Conditional Neural Solvers for Parametric Stochastic-Volatility Pricing](https://mlsanity.com/paper/2610.19254/) (2026)

## 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.