# NewPINNs: Physics-Informing Neural Networks Using Conventional Solvers for Partial Differential Equations

arXiv: https://arxiv.org/abs/2601.17207 · HTML: https://mlsanity.com/paper/2601.17207/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 23 of its 87 references that are in the map.
- First posted on arXiv 23 Jan 2026.

## Builds on (most cited first, 23 of 23)

- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [Deep Equilibrium Models](https://mlsanity.com/paper/1909.01377/) (2019)
- [Universal Differential Equations for Scientific Machine Learning](https://mlsanity.com/paper/2001.04385/) (2020)
- [Deep Hidden Physics Models: Deep Learning of Nonlinear Partial Differential Equations](https://mlsanity.com/paper/1801.06637/) (2018)
- [PDE-Net 2.0: Learning PDEs from Data with A Numeric-Symbolic Hybrid Deep Network](https://mlsanity.com/paper/1812.04426/) (2018)
- [Multiscale Deep Equilibrium Models](https://mlsanity.com/paper/2006.08656/) (2020)
- [Challenges in Training PINNs: A Loss Landscape Perspective](https://mlsanity.com/paper/2402.01868/) (2024)
- [Physics-informed graph neural Galerkin networks: A unified framework for solving PDE-governed forward and inverse problems](https://mlsanity.com/paper/2107.12146/) (2021)
- [Monotone operator equilibrium networks](https://mlsanity.com/paper/2006.08591/) (2020)
- [Blending Neural Operators and Relaxation Methods in PDE Numerical Solvers](https://mlsanity.com/paper/2208.13273/) (2022)
- [Rethinking materials simulations: Blending direct numerical simulations with neural operators](https://mlsanity.com/paper/2312.05410/) (2023)
- [Deep Equilibrium Based Neural Operators for Steady-State PDEs](https://mlsanity.com/paper/2312.00234/) (2023)
- [Discovery of partial differential equations from highly noisy and sparse data with physics-informed information criterion](https://mlsanity.com/paper/2208.03322/) (2022)
- [Deep-OSG: Deep Learning of Operators in Semigroup](https://mlsanity.com/paper/2302.03358/) (2023)
- [XLB: A differentiable massively parallel lattice Boltzmann library in Python](https://mlsanity.com/paper/2311.16080/) (2023)
- [Physics-Informed Neural Networks for High-Frequency and Multi-Scale Problems using Transfer Learning](https://mlsanity.com/paper/2401.02810/) (2024)
- [Data-driven Identification of 2D Partial Differential Equations using extracted physical features](https://mlsanity.com/paper/2010.10626/) (2020)
- [Neural-Initialized Newton: Accelerating Nonlinear Finite Elements via Operator Learning](https://mlsanity.com/paper/2511.06802/) (2025)

## Abstract (arXiv)

We introduce NewPINNs, a physics-informing learning framework that couples neural networks with conventional numerical solvers for solving differential equations. Rather than enforcing governing equations and boundary conditions through residual-based loss terms, NewPINNs integrates the solver directly into the training loop and defines learning objectives through solver-consistency. The neural network produces candidate solution states that are advanced by the numerical solver, and training minimizes the discrepancy between the network prediction and the solver-evolved state. This pull-push interaction enables the network to learn physically admissible solutions through repeated exposure to the solver's action, without requiring problem-specific loss engineering or explicit evaluation of differential equation residuals. By delegating the enforcement of physics, boundary conditions, and numerical stability to established numerical solvers, NewPINNs mitigates several well-known failure modes of standard physics-informed neural networks, including optimization pathologies, sensitivity to loss weighting, and poor performance in stiff or nonlinear regimes. We demonstrate the effectiveness of the proposed approach across multiple forward and inverse problems involving finite volume, finite element, and spectral solvers.