# PILIR: Physics-Informed Local Implicit Representation

arXiv: https://arxiv.org/abs/2605.00385 · HTML: https://mlsanity.com/paper/2605.00385/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 19 of its 30 references that are in the map.
- First posted on arXiv 1 May 2026.

## Builds on (most cited first, 19 of 19)

- [Instant Neural Graphics Primitives with a Multiresolution Hash Encoding](https://mlsanity.com/paper/2201.05989/) (2022)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [K-Planes: Explicit Radiance Fields in Space, Time, and Appearance](https://mlsanity.com/paper/2301.10241/) (2023)
- [When and why PINNs fail to train: A neural tangent kernel perspective](https://mlsanity.com/paper/2007.14527/) (2020)
- [Learning Continuous Image Representation with Local Implicit Image Function](https://mlsanity.com/paper/2012.09161/) (2020)
- [On the eigenvector bias of Fourier feature networks: From regression to solving multi-scale PDEs with physics-informed neural networks](https://mlsanity.com/paper/2012.10047/) (2020)
- [WIRE: Wavelet Implicit Neural Representations](https://mlsanity.com/paper/2301.05187/) (2023)
- [Implicit Diffusion Models for Continuous Super-Resolution](https://mlsanity.com/paper/2303.16491/) (2023)
- [Integrating Scientific Knowledge with Machine Learning for Engineering and Environmental Systems](https://mlsanity.com/paper/2003.04919/) (2020)
- [Overview frequency principle/spectral bias in deep learning](https://mlsanity.com/paper/2201.07395/) (2022)
- [Kolmogorov Arnold Informed neural network: A physics-informed deep learning framework for solving forward and inverse problems based on Kolmogorov Arnold Networks](https://mlsanity.com/paper/2406.11045/) (2024)
- [ConFIG: Towards Conflict-free Training of Physics Informed Neural Networks](https://mlsanity.com/paper/2408.11104/) (2024)
- [Spectral Bias in Practice: The Role of Function Frequency in Generalization](https://mlsanity.com/paper/2110.02424/) (2021)
- [PIXEL: Physics-Informed Cell Representations for Fast and Accurate PDE Solvers](https://mlsanity.com/paper/2207.12800/) (2022)
- [Score-Based Physics-Informed Neural Networks for High-Dimensional Fokker-Planck Equations](https://mlsanity.com/paper/2402.07465/) (2024)
- [PIG: Physics-Informed Gaussians as Adaptive Parametric Mesh Representations](https://mlsanity.com/paper/2412.05994/) (2024)
- [Parametric Encoding with Attention and Convolution Mitigate Spectral Bias of Neural Partial Differential Equation Solvers](https://mlsanity.com/paper/2403.15652/) (2024)
- [Dual-Balancing for Physics-Informed Neural Networks](https://mlsanity.com/paper/2505.11117/) (2025)
- [Physics informed cell representations for variational formulation of multiscale problems](https://mlsanity.com/paper/2405.16770/) (2024)

## Abstract (arXiv)

Physics-Informed Neural Networks have become a powerful mesh-free method for solving partial differential equations, but their performance is often limited by spectral bias. Specifically, in standard MLPs used in PINNs, the global parameter coupling causes the model to prioritize learning low-frequency components, resulting in slow convergence for high-frequency details. To overcome this limitation, we introduce the Physics-Informed Local Implicit Representation (PILIR). Our approach separates the global physical domain into a discrete latent feature space and a continuous generative decoder. By using a learnable grid to encode explicit spatial locality, PILIR can capture high-frequency details locally, preventing dilution by global patterns. A generative neural operator then synthesizes these local latent features into continuous physical fields, allowing accurate reconstruction of fine-scale structures. Experiments on a range of challenging PDEs show that PILIR effectively mitigates spectral bias, thereby boosting the convergence of high-frequency details and achieving superior accuracy compared to state-of-the-art methods.