# Active learning of deep surrogates for PDEs: Application to metasurface design

arXiv: https://arxiv.org/abs/2008.12649 · HTML: https://mlsanity.com/paper/2008.12649/

## Key facts

- Cited by 28 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Aug 2020.

## Built on by (most cited first, 28 of 28)

- [Physics-informed neural networks with hard constraints for inverse design](https://mlsanity.com/paper/2102.04626/) (2021)
- [Physics-Informed Machine Learning: A Survey on Problems, Methods and Applications](https://mlsanity.com/paper/2211.08064/) (2022)
- [Active Learning for Neural PDE Solvers](https://mlsanity.com/paper/2408.01536/) (2024)
- [A neural operator-based surrogate solver for free-form electromagnetic inverse design](https://mlsanity.com/paper/2302.01934/) (2023)
- [Physics-enhanced deep surrogates for partial differential equations](https://mlsanity.com/paper/2111.05841/) (2021)
- [Differentiable Physics: A Position Piece](https://mlsanity.com/paper/2109.07573/) (2021)
- [TNet: A Model-Constrained Tikhonov Network Approach for Inverse Problems](https://mlsanity.com/paper/2105.12033/) (2021)
- [Solving multiphysics-based inverse problems with learned surrogates and constraints](https://mlsanity.com/paper/2307.11099/) (2023)
- [Inverse Design in Nanophotonics via Representation Learning](https://mlsanity.com/paper/2507.00546/) (2025)
- [Failure-averse Active Learning for Physics-constrained Systems](https://mlsanity.com/paper/2110.14443/) (2021)
- [Deep Convolutional Neural Networks to Predict Mutual Coupling Effects in Metasurfaces](https://mlsanity.com/paper/2102.01761/) (2021)
- [Feasibility Study on Active Learning of Smart Surrogates for Scientific Simulations](https://mlsanity.com/paper/2407.07674/) (2024)
- [Active Learning with Selective Time-Step Acquisition for PDEs](https://mlsanity.com/paper/2511.18107/) (2025)
- [Inverse Design of Grating Couplers Using the Policy Gradient Method from Reinforcement Learning](https://mlsanity.com/paper/2107.00088/) (2021)
- [Programming with Neural Surrogates of Programs](https://mlsanity.com/paper/2112.06148/) (2021)
- [A Model-Constrained Tangent Slope Learning Approach for Dynamical Systems](https://mlsanity.com/paper/2208.04995/) (2022)
- [Physics and geometry informed neural operator network with application to acoustic scattering](https://mlsanity.com/paper/2406.03407/) (2024)
- [Learning Where to Simulate: Generative Active Sampling for Online PDE Surrogate Training](https://mlsanity.com/paper/2606.09949/) (2026)
- [VI-PINNs: Variance-involved Physics-informed Neural Networks for Fast and Accurate Prediction of Partial Differential Equations](https://mlsanity.com/paper/2211.16753/) (2022)
- [Can AI Follow In Einstein's Footsteps?](https://mlsanity.com/paper/2607.27794/) (2026)
- [Turaco: Complexity-Guided Data Sampling for Training Neural Surrogates of Programs](https://mlsanity.com/paper/2309.11726/) (2023)
- [Reinforcement learning framework for the mechanical design of microelectronic components under multiphysics constraints](https://mlsanity.com/paper/2504.17142/) (2025)
- [Learning task-specific predictive models for scientific computing](https://mlsanity.com/paper/2506.03835/) (2025)
- [Neural surrogates for designing gravitational wave detectors](https://mlsanity.com/paper/2511.19364/) (2025)
- [Physics Enhanced Deep Surrogates for the Phonon Boltzmann Transport Equation](https://mlsanity.com/paper/2512.05976/) (2025)
- [Active learning for photonic crystals](https://mlsanity.com/paper/2601.16287/) (2026)
- [Data-Efficient Neural Operator Training via Physics-Based Active Learning](https://mlsanity.com/paper/2605.21348/) (2026)
- [Inductively Scalable, Single-Step Neural Surrogates for Wave-Scattering Inverse Problems](https://mlsanity.com/paper/2608.17344/) (2026)

## Abstract (arXiv)

Surrogate models for partial-differential equations are widely used in the design of meta-materials to rapidly evaluate the behavior of composable components. However, the training cost of accurate surrogates by machine learning can rapidly increase with the number of variables. For photonic-device models, we find that this training becomes especially challenging as design regions grow larger than the optical wavelength. We present an active learning algorithm that reduces the number of training points by more than an order of magnitude for a neural-network surrogate model of optical-surface components compared to random samples. Results show that the surrogate evaluation is over two orders of magnitude faster than a direct solve, and we demonstrate how this can be exploited to accelerate large-scale engineering optimization.