# Physics-Guided Dimension Reduction for Simulation-Free Operator Learning of Stiff Differential-Algebraic Systems

arXiv: https://arxiv.org/abs/2604.19930 · HTML: https://mlsanity.com/paper/2604.19930/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 32 references that are in the map.
- First posted on arXiv 21 Apr 2026.

## Builds on (most cited first, 18 of 18)

- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [Conformalized Quantile Regression](https://mlsanity.com/paper/1905.03222/) (2019)
- [Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets](https://mlsanity.com/paper/2103.10974/) (2021)
- [Adaptive Conformal Inference Under Distribution Shift](https://mlsanity.com/paper/2106.00170/) (2021)
- [DC3: A learning method for optimization with hard constraints](https://mlsanity.com/paper/2104.12225/) (2021)
- [Enhanced Physics-Informed Neural Networks with Augmented Lagrangian Relaxation Method (AL-PINNs)](https://mlsanity.com/paper/2205.01059/) (2022)
- [DeepONet-Grid-UQ: A Trustworthy Deep Operator Framework for Predicting the Power Grid's Post-Fault Trajectories](https://mlsanity.com/paper/2202.07176/) (2022)
- [DAE-PINN: A Physics-Informed Neural Network Model for Simulating Differential-Algebraic Equations with Application to Power Networks](https://mlsanity.com/paper/2109.04304/) (2021)
- [Stabilized Neural Differential Equations for Learning Dynamics with Explicit Constraints](https://mlsanity.com/paper/2306.09739/) (2023)
- [PINNSim: A Simulator for Power System Dynamics based on Physics-Informed Neural Networks](https://mlsanity.com/paper/2303.10256/) (2023)
- [Learning Neural Differential Algebraic Equations via Operator Splitting](https://mlsanity.com/paper/2403.12938/) (2024)
- [Physics-Informed Neural Networks with Trust-Region Sequential Quadratic Programming](https://mlsanity.com/paper/2409.10777/) (2024)
- [Constrained Optimization From a Control Perspective via Feedback Linearization](https://mlsanity.com/paper/2503.12665/) (2025)
- [A Simultaneous Approach for Training Neural Differential-Algebraic Systems of Equations](https://mlsanity.com/paper/2504.04665/) (2025)
- [Semi-Explicit Neural DAEs: Learning Long-Horizon Dynamical Systems with Algebraic Constraints](https://mlsanity.com/paper/2505.20515/) (2025)
- [Hard-Constrained Neural Networks with Physics-Embedded Architecture for Residual Dynamics Learning and Invariant Enforcement in Cyber-Physical Systems](https://mlsanity.com/paper/2511.23307/) (2025)
- [DAE-HardNet: A Physics Constrained Neural Network Enforcing Differential-Algebraic Hard Constraints](https://mlsanity.com/paper/2512.05881/) (2025)
- [Neural Operators for Power Systems: A Physics-Informed Framework for Modeling Power System Components](https://mlsanity.com/paper/2511.05216/) (2025)

## Built on by (most cited first, 1 of 1)

- [A Unified Mamba--MoE Surrogate for Closed-Loop Simulation and Measurement-Window Forecasting of Inverter Transients](https://mlsanity.com/paper/2608.15051/) (2026)

## Abstract (arXiv)

Neural surrogates for stiff differential-algebraic equations (DAEs) face two barriers: soft-constraint methods leave algebraic residuals that stiffness amplifies into errors, and hard-constraint methods require trajectory data from stiff integrators. We introduce an extended Newton implicit layer that enforces algebraic constraints exactly and reduces fast dynamics to their quasi-steady-state values in a single differentiable solve. Embedded in a physics-informed DeepONet, the layer recovers all fast and algebraic states exactly from slow-state predictions, removes the per-window stiffness-amplification pathway, and yields a stiffness-scaled Implicit Function Theorem gradient absent from penalty methods. Cascaded implicit layers extend this to multi-component systems with provable convergence. On a grid-forming inverter (stiffness ratio of about 4712), extended Newton attains 1.42% error versus 39.3% (penalty) and 57.0% (standard Newton); augmented Lagrangian and feedback linearization diverged. Two independently trained models compose without retraining (0.72% to 1.16% error, exact constraint satisfaction). Cross-domain validation on the Robertson stiff DAE (stiffness ratio up to 105) confirms generalization. Conformal prediction provides 90% coverage with automatic out-of-distribution detection.