# Dual-Balancing for Physics-Informed Neural Networks

arXiv: https://arxiv.org/abs/2505.11117 · HTML: https://mlsanity.com/paper/2505.11117/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 36 references that are in the map.
- First posted on arXiv 16 May 2025.

## Builds on (most cited first, 13 of 13)

- [Characterizing possible failure modes in physics-informed neural networks](https://mlsanity.com/paper/2109.01050/) (2021)
- [When and why PINNs fail to train: A neural tangent kernel perspective](https://mlsanity.com/paper/2007.14527/) (2020)
- [A comprehensive study of non-adaptive and residual-based adaptive sampling for physics-informed neural networks](https://mlsanity.com/paper/2207.10289/) (2022)
- [Self-Adaptive Physics-Informed Neural Networks using a Soft Attention Mechanism](https://mlsanity.com/paper/2009.04544/) (2020)
- [Mitigating Propagation Failures in Physics-informed Neural Networks using Retain-Resample-Release (R3) Sampling](https://mlsanity.com/paper/2207.02338/) (2022)
- [A Dual-Dimer Method for Training Physics-Constrained Neural Networks with Minimax Architecture](https://mlsanity.com/paper/2005.00615/) (2020)
- [DPM: A Novel Training Method for Physics-Informed Neural Networks in Extrapolation](https://mlsanity.com/paper/2012.02681/) (2020)
- [Inverse-Dirichlet Weighting Enables Reliable Training of Physics Informed Neural Networks](https://mlsanity.com/paper/2107.00940/) (2021)
- [Spline-PINN: Approaching PDEs without Data using Fast, Physics-Informed Hermite-Spline CNNs](https://mlsanity.com/paper/2109.07143/) (2021)
- [Multi-Loss Weighting with Coefficient of Variations](https://mlsanity.com/paper/2009.01717/) (2020)
- [Physics-Informed Graph Neural Networks for Water Distribution Systems](https://mlsanity.com/paper/2403.18570/) (2024)
- [Structure-Preserving Physics-Informed Neural Networks With Energy or Lyapunov Structure](https://mlsanity.com/paper/2401.04986/) (2024)
- [Physics-Informed Neural Networks: Minimizing Residual Loss with Wide Networks and Effective Activations](https://mlsanity.com/paper/2405.01680/) (2024)

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

- [Boundary condition enforcement with PINNs: a comparative study and verification on 3D geometries](https://mlsanity.com/paper/2512.14941/) (2025)
- [Enhancing PINN Accuracy for the RLW Equation: Adaptive and Conservative Approaches](https://mlsanity.com/paper/2511.11638/) (2025)
- [PILIR: Physics-Informed Local Implicit Representation](https://mlsanity.com/paper/2605.00385/) (2026)
- [Mitigating Gradient Pathology in PINNs through Aligned Constraint](https://mlsanity.com/paper/2605.25001/) (2026)
- [Learning to Distributedly Estimate under Partially Known Dynamics: A Covariance-Agnostic Neural Kalman Consensus Filter](https://mlsanity.com/paper/2606.28441/) (2026)

## Abstract (arXiv)

Physics-informed neural networks (PINNs) have emerged as a new learning paradigm for solving partial differential equations (PDEs) by enforcing the constraints of physical equations, boundary conditions (BCs), and initial conditions (ICs) into the loss function. Despite their successes, vanilla PINNs still suffer from poor accuracy and slow convergence due to the intractable multi-objective optimization issue. In this paper, we propose a novel Dual-Balanced PINN (DB-PINN), which dynamically adjusts loss weights by integrating inter-balancing and intra-balancing to alleviate two imbalance issues in PINNs. Inter-balancing aims to mitigate the gradient imbalance between PDE residual loss and condition-fitting losses by determining an aggregated weight that offsets their gradient distribution discrepancies. Intra-balancing acts on condition-fitting losses to tackle the imbalance in fitting difficulty across diverse conditions. By evaluating the fitting difficulty based on the loss records, intra-balancing can allocate the aggregated weight proportionally to each condition loss according to its fitting difficulty level. We further introduce a robust weight update strategy to prevent abrupt spikes and arithmetic overflow in instantaneous weight values caused by large loss variances, enabling smooth weight updating and stable training. Extensive experiments demonstrate that DB-PINN achieves significantly superior performance than those popular gradient-based weighting methods in terms of convergence speed and prediction accuracy. Our code and supplementary material are available at https://github.com/chenhong-zhou/DualBalanced-PINNs.