# Time Resolution Independent Operator Learning

arXiv: https://arxiv.org/abs/2507.02524 · HTML: https://mlsanity.com/paper/2507.02524/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Jul 2025.

## Built on by (most cited first, 5 of 5)

- [A Physics-informed Multi-resolution Neural Operator](https://mlsanity.com/paper/2510.23810/) (2025)
- [Physics-Audited Agentic Discovery in Scientific Machine Learning](https://mlsanity.com/paper/2607.07379/) (2026)
- [ANCHOR: Error-Controlled Adaptive Numerical Correction for Neural Operator Time Marching](https://mlsanity.com/paper/2512.19643/) (2025)
- [Learning Heat-based Equations in Self-similar variables](https://mlsanity.com/paper/2602.00872/) (2026)
- [No Free Lunch in Flow Surrogates under Time-Varying Boundary Conditions: A Two-Regime Study](https://mlsanity.com/paper/2607.23667/) (2026)

## Abstract (arXiv)

Accurately learning solution operators for time-dependent partial differential equations (PDEs) from sparse and irregular data remains a challenging task. Recurrent DeepONet extensions inherit the discrete-time limitations of sequence-to-sequence (seq2seq) RNN architectures, while neural-ODE surrogates cannot incorporate new inputs after initialization. We introduce NCDE-DeepONet, a continuous-time operator network that embeds a Neural Controlled Differential Equation (NCDE) in the branch and augments the trunk with explicit space-time coordinates. The NCDE encodes an entire load history as the solution of a controlled ODE driven by a spline-interpolated input path, making the representation input-resolution-independent: it encodes different input signal discretizations of the observed samples. The trunk then probes this latent path at arbitrary spatial locations and times, rendering the overall map output-resolution independent: predictions can be queried on meshes and time steps unseen during training without retraining or interpolation. Benchmarks on transient Poisson, elastodynamic, and thermoelastic problems confirm the robustness and accuracy of the framework, achieving almost instant solution prediction. These findings suggest that controlled dynamics provide a principled and efficient foundation for high-fidelity operator learning in transient mechanics.