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ApjY32f3Xr | PINNacle: A Comprehensive Benchmark of Physics-Informed Neural Networks for Solving PDEs | 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 data... | Under review as a conference paper at ICLR 2024
PINN ACLE : A C OMPREHENSIVE BENCHMARK OF
PHYSICS -INFORMED NEURAL NETWORKS FOR SOLV-
ING PDE S
Anonymous authors
Paper under double-blind review
ABSTRACT
While significant progress has been made on Physics-Informed Neural Networks
(PINNs), a comprehensive comparison of t... | Zhongkai Hao, Jiachen Yao, Chang Su, Hang Su, Ziao Wang, Fanzhi Lu, Zeyu Xia, Yichi Zhang, Songming Liu, Lu Lu, Jun Zhu | Reject | 2,024 | {"id": "ApjY32f3Xr", "forum": "ApjY32f3Xr", "content": {"title": {"value": "PINNacle: A Comprehensive Benchmark of Physics-Informed Neural Networks for Solving PDEs"}, "authors": {"value": ["Zhongkai Hao", "Jiachen Yao", "Chang Su", "Hang Su", "Ziao Wang", "Fanzhi Lu", "Zeyu Xia", "Yichi Zhang", "Songming Liu", "Lu Lu"... | [Summary]:
This paper provides both a collection of benchmark datasets as well as a standardized suite of PINN-type neural network PDE solution approximators arranged as a python package.
It further shows benchmark numbers of the different PINN methods on the benchmark datasets.
[Strengths]:
Providing any meaningful ... | ICLR.cc/2024/Conference/Submission9493/Reviewer_Ytqc | 6 | 3 | {"id": "Ait2z7EwaE", "forum": "ApjY32f3Xr", "replyto": "ApjY32f3Xr", "content": {"summary": {"value": "This paper provides both a collection of benchmark datasets as well as a standardized suite of PINN-type neural network PDE solution approximators arranged as a python package.\n\nIt further shows benchmark numbers of... | {
"criticism": 3,
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"praise": 3,
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"results_and_discussion": 2,
"suggestion_and_solution": 14,
"total": 27
} | 1.888889 | -1.204467 | 3.093356 | 1.926865 | 0.437026 | 0.037976 | 0.111111 | 0.037037 | 0.111111 | 0.814815 | 0.111111 | 0.111111 | 0.074074 | 0.518519 | {
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"suggestion_and_... | 1.888889 | iclr2024 | openreview | 0 | 0 | 0 | null | ||
ApjY32f3Xr | PINNacle: A Comprehensive Benchmark of Physics-Informed Neural Networks for Solving PDEs | 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 data... | Under review as a conference paper at ICLR 2024
PINN ACLE : A C OMPREHENSIVE BENCHMARK OF
PHYSICS -INFORMED NEURAL NETWORKS FOR SOLV-
ING PDE S
Anonymous authors
Paper under double-blind review
ABSTRACT
While significant progress has been made on Physics-Informed Neural Networks
(PINNs), a comprehensive comparison of t... | Zhongkai Hao, Jiachen Yao, Chang Su, Hang Su, Ziao Wang, Fanzhi Lu, Zeyu Xia, Yichi Zhang, Songming Liu, Lu Lu, Jun Zhu | Reject | 2,024 | {"id": "ApjY32f3Xr", "forum": "ApjY32f3Xr", "content": {"title": {"value": "PINNacle: A Comprehensive Benchmark of Physics-Informed Neural Networks for Solving PDEs"}, "authors": {"value": ["Zhongkai Hao", "Jiachen Yao", "Chang Su", "Hang Su", "Ziao Wang", "Fanzhi Lu", "Zeyu Xia", "Yichi Zhang", "Songming Liu", "Lu Lu"... | [Summary]:
This paper provides a comprehensive comparison of PINN training methods, problems, and data. The paper visits common problems with training PINNs, namely the complex geometry, the multi-scale phenomena, nonlinearity of some PDE ofrs, and the high dimensional PDE problems. They also provide various training m... | ICLR.cc/2024/Conference/Submission9493/Reviewer_RGvf | 6 | 3 | {"id": "CZ5Y4HIwQW", "forum": "ApjY32f3Xr", "replyto": "ApjY32f3Xr", "content": {"summary": {"value": "This paper provides a comprehensive comparison of PINN training methods, problems, and data. The paper visits common problems with training PINNs, namely the complex geometry, the multi-scale phenomena, nonlinearity o... | {
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"example": 0,
"importance_and_relevance": 4,
"materials_and_methods": 8,
"praise": 9,
"presentation_and_reporting": 7,
"results_and_discussion": 4,
"suggestion_and_solution": 3,
"total": 29
} | 1.344828 | -2.695474 | 4.040302 | 1.369971 | 0.260754 | 0.025144 | 0.137931 | 0 | 0.137931 | 0.275862 | 0.310345 | 0.241379 | 0.137931 | 0.103448 | {
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"results_and_discussion": 0.13793103448275862,
"suggestion_and_solution": 0.103... | 1.344828 | iclr2024 | openreview | 0 | 0 | 0 | null | ||
ApjY32f3Xr | PINNacle: A Comprehensive Benchmark of Physics-Informed Neural Networks for Solving PDEs | "While significant progress has been made on Physics-Informed Neural Networks (PINNs), a comprehensi(...TRUNCATED) | "Under review as a conference paper at ICLR 2024\nPINN ACLE : A C OMPREHENSIVE BENCHMARK OF\nPHYSICS(...TRUNCATED) | "Zhongkai Hao, Jiachen Yao, Chang Su, Hang Su, Ziao Wang, Fanzhi Lu, Zeyu Xia, Yichi Zhang, Songming(...TRUNCATED) | Reject | 2,024 | "{\"id\": \"ApjY32f3Xr\", \"forum\": \"ApjY32f3Xr\", \"content\": {\"title\": {\"value\": \"PINNacle(...TRUNCATED) | "[Summary]:\nThe paper provides a benchmarking tool called PINNacle which was lacking in the domain (...TRUNCATED) | ICLR.cc/2024/Conference/Submission9493/Reviewer_oeuE | 3 | 5 | "{\"id\": \"4e1fSBB3OO\", \"forum\": \"ApjY32f3Xr\", \"replyto\": \"ApjY32f3Xr\", \"content\": {\"su(...TRUNCATED) | {"criticism":5,"example":0,"importance_and_relevance":1,"materials_and_methods":10,"praise":2,"prese(...TRUNCATED) | 1.090909 | -0.187468 | 1.278377 | 1.111025 | 0.196675 | 0.020116 | 0.227273 | 0 | 0.045455 | 0.454545 | 0.090909 | 0.090909 | 0.136364 | 0.045455 | {"criticism":0.22727272727272727,"example":0.0,"importance_and_relevance":0.045454545454545456,"mate(...TRUNCATED) | 1.090909 | iclr2024 | openreview | 0 | 0 | 0 | null | ||
ApjY32f3Xr | PINNacle: A Comprehensive Benchmark of Physics-Informed Neural Networks for Solving PDEs | "While significant progress has been made on Physics-Informed Neural Networks (PINNs), a comprehensi(...TRUNCATED) | "Under review as a conference paper at ICLR 2024\nPINN ACLE : A C OMPREHENSIVE BENCHMARK OF\nPHYSICS(...TRUNCATED) | "Zhongkai Hao, Jiachen Yao, Chang Su, Hang Su, Ziao Wang, Fanzhi Lu, Zeyu Xia, Yichi Zhang, Songming(...TRUNCATED) | Reject | 2,024 | "{\"id\": \"ApjY32f3Xr\", \"forum\": \"ApjY32f3Xr\", \"content\": {\"title\": {\"value\": \"PINNacle(...TRUNCATED) | "[Summary]:\nThe article introduces \"PINNacle\", a robust benchmark suite tailored for Physics-Info(...TRUNCATED) | ICLR.cc/2024/Conference/Submission9493/Reviewer_xNZs | 6 | 3 | "{\"id\": \"C4sqXJNESI\", \"forum\": \"ApjY32f3Xr\", \"replyto\": \"ApjY32f3Xr\", \"content\": {\"su(...TRUNCATED) | {"criticism":1,"example":0,"importance_and_relevance":12,"materials_and_methods":30,"praise":8,"pres(...TRUNCATED) | 1.625 | -9.880391 | 11.505391 | 1.671499 | 0.471897 | 0.046499 | 0.025 | 0 | 0.3 | 0.75 | 0.2 | 0 | 0.2 | 0.15 | {"criticism":0.025,"example":0.0,"importance_and_relevance":0.3,"materials_and_methods":0.75,"praise(...TRUNCATED) | 1.625 | iclr2024 | openreview | 0 | 0 | 0 | null | ||
mnyXZBa5dP | "Image Authenticity Detection using Eye Gazing Data: A Performance Comparison Beyond Human Capabili(...TRUNCATED) | "In the digital age, determining the authenticity of images has become \nincreasingly crucial. This (...TRUNCATED) | Ping Zhang | Unknown | 2,024 | "{\"id\": \"mnyXZBa5dP\", \"forum\": \"mnyXZBa5dP\", \"content\": {\"title\": {\"value\": \"Image Au(...TRUNCATED) | N/A | null | null | {} | {"criticism":0,"example":0,"importance_and_relevance":0,"materials_and_methods":0,"praise":0,"presen(...TRUNCATED) | -10 | -2.667231 | 2.667231 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | {"criticism":0.0,"example":0.0,"importance_and_relevance":0.0,"materials_and_methods":0.0,"praise":0(...TRUNCATED) | -10 | iclr2024 | openreview | 0 | 0 | 0 | null | ||||
kKRbAY4CXv | Neural Evolutionary Kernel Method: A Knowledge-Based Learning Architechture for Evolutionary PDEs | "Numerical solution of partial differential equations (PDEs) plays a vital role in various fields of(...TRUNCATED) | "Under review as a conference paper at ICLR 2024\nNEURAL EVOLUTIONARY KERNEL METHOD :\nA K NOWLEDGE (...TRUNCATED) | Shuo Ling, Wenjun Ying, Zhen Zhang | Reject | 2,024 | "{\"id\": \"kKRbAY4CXv\", \"forum\": \"kKRbAY4CXv\", \"content\": {\"title\": {\"value\": \"Neural E(...TRUNCATED) | "[Summary]:\nThe paper introduces a novel approach called Neural Evolutionary Kernel Method (NEKM) f(...TRUNCATED) | ICLR.cc/2024/Conference/Submission9498/Reviewer_71KZ | 6 | 2 | "{\"id\": \"hZLx3fXD5m\", \"forum\": \"kKRbAY4CXv\", \"replyto\": \"kKRbAY4CXv\", \"content\": {\"su(...TRUNCATED) | {"criticism":5,"example":0,"importance_and_relevance":30,"materials_and_methods":56,"praise":20,"pre(...TRUNCATED) | 1.39 | -118.067211 | 119.457211 | 1.447648 | 0.561711 | 0.057648 | 0.05 | 0 | 0.3 | 0.56 | 0.2 | 0.01 | 0.15 | 0.12 | {"criticism":0.05,"example":0.0,"importance_and_relevance":0.3,"materials_and_methods":0.56,"praise"(...TRUNCATED) | 1.39 | iclr2024 | openreview | 0 | 0 | 0 | null | ||
kKRbAY4CXv | Neural Evolutionary Kernel Method: A Knowledge-Based Learning Architechture for Evolutionary PDEs | "Numerical solution of partial differential equations (PDEs) plays a vital role in various fields of(...TRUNCATED) | "Under review as a conference paper at ICLR 2024\nNEURAL EVOLUTIONARY KERNEL METHOD :\nA K NOWLEDGE (...TRUNCATED) | Shuo Ling, Wenjun Ying, Zhen Zhang | Reject | 2,024 | "{\"id\": \"kKRbAY4CXv\", \"forum\": \"kKRbAY4CXv\", \"content\": {\"title\": {\"value\": \"Neural E(...TRUNCATED) | "[Summary]:\nThis paper aims to tackle solving partial differential equations (PDEs) traditionally s(...TRUNCATED) | ICLR.cc/2024/Conference/Submission9498/Reviewer_sX1E | 5 | 4 | "{\"id\": \"eSJOZmZeDG\", \"forum\": \"kKRbAY4CXv\", \"replyto\": \"kKRbAY4CXv\", \"content\": {\"su(...TRUNCATED) | {"criticism":5,"example":2,"importance_and_relevance":2,"materials_and_methods":30,"praise":6,"prese(...TRUNCATED) | 1.807692 | -22.197383 | 24.005076 | 1.843615 | 0.396839 | 0.035923 | 0.096154 | 0.038462 | 0.038462 | 0.576923 | 0.115385 | 0.365385 | 0.153846 | 0.423077 | {"criticism":0.09615384615384616,"example":0.038461538461538464,"importance_and_relevance":0.0384615(...TRUNCATED) | 1.807692 | iclr2024 | openreview | 0 | 0 | 0 | null | ||
kKRbAY4CXv | Neural Evolutionary Kernel Method: A Knowledge-Based Learning Architechture for Evolutionary PDEs | "Numerical solution of partial differential equations (PDEs) plays a vital role in various fields of(...TRUNCATED) | "Under review as a conference paper at ICLR 2024\nNEURAL EVOLUTIONARY KERNEL METHOD :\nA K NOWLEDGE (...TRUNCATED) | Shuo Ling, Wenjun Ying, Zhen Zhang | Reject | 2,024 | "{\"id\": \"kKRbAY4CXv\", \"forum\": \"kKRbAY4CXv\", \"content\": {\"title\": {\"value\": \"Neural E(...TRUNCATED) | "[Summary]:\nThe paper presents the Neural Evolutionary Kernel Method (NEKM) for solving semi-linear(...TRUNCATED) | ICLR.cc/2024/Conference/Submission9498/Reviewer_Ljfw | 3 | 4 | "{\"id\": \"uwuFudLbCi\", \"forum\": \"kKRbAY4CXv\", \"replyto\": \"kKRbAY4CXv\", \"content\": {\"su(...TRUNCATED) | {"criticism":3,"example":1,"importance_and_relevance":2,"materials_and_methods":12,"praise":1,"prese(...TRUNCATED) | 1.647059 | 1.39454 | 0.252519 | 1.662162 | 0.212119 | 0.015103 | 0.176471 | 0.058824 | 0.117647 | 0.705882 | 0.058824 | 0.058824 | 0.117647 | 0.352941 | {"criticism":0.17647058823529413,"example":0.058823529411764705,"importance_and_relevance":0.1176470(...TRUNCATED) | 1.647059 | iclr2024 | openreview | 0 | 0 | 0 | null | ||
kKRbAY4CXv | Neural Evolutionary Kernel Method: A Knowledge-Based Learning Architechture for Evolutionary PDEs | "Numerical solution of partial differential equations (PDEs) plays a vital role in various fields of(...TRUNCATED) | "Under review as a conference paper at ICLR 2024\nNEURAL EVOLUTIONARY KERNEL METHOD :\nA K NOWLEDGE (...TRUNCATED) | Shuo Ling, Wenjun Ying, Zhen Zhang | Reject | 2,024 | "{\"id\": \"kKRbAY4CXv\", \"forum\": \"kKRbAY4CXv\", \"content\": {\"title\": {\"value\": \"Neural E(...TRUNCATED) | "[Summary]:\nThis paper proposes a neural network-based algorithm, namely the Neural Evolutionary Ke(...TRUNCATED) | ICLR.cc/2024/Conference/Submission9498/Reviewer_tJtQ | 3 | 3 | "{\"id\": \"u9bOLSB5vz\", \"forum\": \"kKRbAY4CXv\", \"replyto\": \"kKRbAY4CXv\", \"content\": {\"su(...TRUNCATED) | {"criticism":5,"example":0,"importance_and_relevance":1,"materials_and_methods":12,"praise":3,"prese(...TRUNCATED) | 1.526316 | 0.958148 | 0.568167 | 1.538009 | 0.129803 | 0.011693 | 0.263158 | 0 | 0.052632 | 0.631579 | 0.157895 | 0.105263 | 0.263158 | 0.052632 | {"criticism":0.2631578947368421,"example":0.0,"importance_and_relevance":0.05263157894736842,"materi(...TRUNCATED) | 1.526316 | iclr2024 | openreview | 0 | 0 | 0 | null | ||
eUgS9Ig8JG | SaNN: Simple Yet Powerful Simplicial-aware Neural Networks | "Simplicial neural networks (SNNs) are deep models for higher-order graph representation learning. S(...TRUNCATED) | "Published as a conference paper at ICLR 2024\nSANN: S IMPLE YET POWERFUL SIMPLICIAL -AWARE\nNEURAL (...TRUNCATED) | Sravanthi Gurugubelli, Sundeep Prabhakar Chepuri | Accept (spotlight) | 2,024 | "{\"id\": \"eUgS9Ig8JG\", \"forum\": \"eUgS9Ig8JG\", \"content\": {\"title\": {\"value\": \"SaNN: Si(...TRUNCATED) | "[Summary]:\nThe paper describes an efficient, and effective approach for learning representations f(...TRUNCATED) | ICLR.cc/2024/Conference/Submission9491/Reviewer_jAzK | 8 | 4 | "{\"id\": \"6iCqDrP0HV\", \"forum\": \"eUgS9Ig8JG\", \"replyto\": \"eUgS9Ig8JG\", \"content\": {\"su(...TRUNCATED) | {"criticism":5,"example":4,"importance_and_relevance":2,"materials_and_methods":10,"praise":6,"prese(...TRUNCATED) | 1.125 | -18.208476 | 19.333476 | 1.138234 | 0.155156 | 0.013234 | 0.104167 | 0.083333 | 0.041667 | 0.208333 | 0.125 | 0.333333 | 0.0625 | 0.166667 | {"criticism":0.10416666666666667,"example":0.08333333333333333,"importance_and_relevance":0.04166666(...TRUNCATED) | 1.125 | iclr2024 | openreview | 0 | 0 | 0 | null |
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