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

Chen-Yang Dai, Che-Chia Chang, Te-Sheng Lin, Ming-Chih Lai, Chieh-Hsin Lai
Proceedings of the 43rd International Conference on Machine Learning, PMLR 306:22358-22384, 2026.

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 relative $L^2$ error and $10\times$ faster convergence compared to PINNs and strong baselines. Code is available at https://github.com/CYDai-ml/TINN.

Cite this Paper

BibTeX
@InProceedings{pmlr-v306-dai26a, title = {{TINN}s: Time-Induced Neural Networks for Solving Time-Dependent {PDE}s}, author = {Dai, Chen-Yang and Chang, Che-Chia and Lin, Te-Sheng and Lai, Ming-Chih and Lai, Chieh-Hsin}, booktitle = {Proceedings of the 43rd International Conference on Machine Learning}, pages = {22358--22384}, year = {2026}, editor = {Zhang, Tong and Dudik, Miroslav and Jaggi, Martin and Agarwal, Alekh and Li, Sharon and Schuurmans, Dale and Zhu, Jerry and Berkenkamp, Felix and Dong, Hanze and Bietti, Alberto}, volume = {306}, series = {Proceedings of Machine Learning Research}, month = {06--11 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v306/main/assets/dai26a/dai26a.pdf}, url = {https://proceedings.mlr.press/v306/dai26a.html}, 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 relative $L^2$ error and $10\times$ faster convergence compared to PINNs and strong baselines. Code is available at https://github.com/CYDai-ml/TINN.} }
Endnote
%0 Conference Paper %T TINNs: Time-Induced Neural Networks for Solving Time-Dependent PDEs %A Chen-Yang Dai %A Che-Chia Chang %A Te-Sheng Lin %A Ming-Chih Lai %A Chieh-Hsin Lai %B Proceedings of the 43rd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2026 %E Tong Zhang %E Miroslav Dudik %E Martin Jaggi %E Alekh Agarwal %E Sharon Li %E Dale Schuurmans %E Jerry Zhu %E Felix Berkenkamp %E Hanze Dong %E Alberto Bietti %F pmlr-v306-dai26a %I PMLR %P 22358--22384 %U https://proceedings.mlr.press/v306/dai26a.html %V 306 %X 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 relative $L^2$ error and $10\times$ faster convergence compared to PINNs and strong baselines. Code is available at https://github.com/CYDai-ml/TINN.
APA
Dai, C., Chang, C., Lin, T., Lai, M. & Lai, C.. (2026). TINNs: Time-Induced Neural Networks for Solving Time-Dependent PDEs. Proceedings of the 43rd International Conference on Machine Learning, in Proceedings of Machine Learning Research 306:22358-22384 Available from https://proceedings.mlr.press/v306/dai26a.html.

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