REVIEW 9 cited by
PINNacle: A Comprehensive Benchmark of Physics-Informed Neural Networks for Solving PDEs
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
read the original abstract
While significant progress has been made on Physics-Informed Neural Networks (PINNs), a comprehensive comparison of these methods across a wide range of Partial Differential Equations (PDEs) is still lacking. This study introduces PINNacle, a benchmarking tool designed to fill this gap. PINNacle provides a diverse dataset, comprising over 20 distinct PDEs from various domains, including heat conduction, fluid dynamics, biology, and electromagnetics. These PDEs encapsulate key challenges inherent to real-world problems, such as complex geometry, multi-scale phenomena, nonlinearity, and high dimensionality. PINNacle also offers a user-friendly toolbox, incorporating about 10 state-of-the-art PINN methods for systematic evaluation and comparison. We have conducted extensive experiments with these methods, offering insights into their strengths and weaknesses. In addition to providing a standardized means of assessing performance, PINNacle also offers an in-depth analysis to guide future research, particularly in areas such as domain decomposition methods and loss reweighting for handling multi-scale problems and complex geometry. To the best of our knowledge, it is the largest benchmark with a diverse and comprehensive evaluation that will undoubtedly foster further research in PINNs.
Forward citations
Cited by 9 Pith papers
-
Continual-Learning Physics-Informed Neural Networks for Parameterized Partial Differential Equations
A continual-learning training scheme with Bayesian task selection, dynamic weighting, and sparse physics replay improves accuracy and query efficiency of parameterized physics-informed neural networks on five benchmarks.
-
BWLer: Barycentric Weight Layer Elucidates a Precision-Conditioning Tradeoff for PINNs
Adding a barycentric interpolation layer to PINNs lifts their precision ceiling, achieving up to 1e-13 relative error on smooth PDEs, while exposing a tradeoff between accuracy and loss conditioning.
-
VideoPDE: Unified Generative PDE Solving via Video Inpainting Diffusion Models
A pixel-space hierarchical video diffusion transformer solves PDE forward, inverse, and sparse-observation tasks by inpainting trajectories, with reported order-of-magnitude error reductions on several 2D benchmark PDEs.
-
Physics-Informed Neural Networks for Solving the Two-Dimensional Shallow Water Equations with Terrain Topography and Rainfall Source Terms
PINNs with a reweighted variable-conservation form solve 2D shallow water cases with rainfall and terrain, but the claimed theoretical superiority is only partially supported.
-
jinns: a JAX Library for Physics-Informed Neural Networks
The paper introduces jinns, a JAX-native PINN library with claimed first-of-its-kind status and superior speed for inverse problems, supported by a small benchmark study.
-
The Well: a Large-Scale Collection of Diverse Physics Simulations for Machine Learning
The Well provides 16 diverse physics simulation datasets totaling 15TB of data, with a unified interface and baselines showing standard surrogate models fail on many of the tasks.
-
PINNsAgent: Automated PDE Surrogation with Large Language Models
An LLM-based multi-agent system that automates PINNs hyperparameter optimization, beating random and Bayesian search on 12 of 14 benchmark PDEs but only matching or beating the PINNacle benchmark on 6 of 14.
-
Principled Approaches for Extending Neural Architectures to Function Spaces for Operator Learning
A practical recipe to convert common neural architectures into discretization-agnostic neural operators, validated by Navier-Stokes experiments showing cross-resolution generalization of FNO-style models.
-
PDE-DKL: PDE-constrained deep kernel learning in high dimensionality
A neural network compresses high-dimensional PDE coordinates into a low-dimensional latent space, where a PDE-constrained Gaussian process achieves accurate solutions and uncertainty estimates on test problems up to 5...
Discussion (0). Continue with ORCID to comment.