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Multi-task learning through composite loss functions is fundamental to modern deep learning, yet optimizing competing objectives remains challenging.
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Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
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Hidden fluid mechanics: Learning velocity and pressure fields from flow visualizations
Maziar Raissi, Alireza Yazdani, and George Em Karniadakis · 2020
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Machine learning in cardiovascular flows modeling: Predicting arterial blood pressure from non-invasive 4D flow MRI data using physics-informed neural networks
Georgios Kissas, Yibo Yang, Eileen Hwuang, Walter R Witschey, John A Detre, and Paris Perdikaris · 2020
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Implicit neural representations with periodic activation functions
Vincent Sitzmann, Julien Martel, Alexander Bergman, David Lindell, and Gordon Wetzstein · 2020
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Adaptive activation functions accelerate convergence in deep and physics-informed neural networks
Ameya D Jagtap, Kenji Kawaguchi, and George Em Karniadakis · 2020
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Solving Allen-Cahn and Cahn-Hilliard equations using the adaptive physics informed neural networks
Colby L Wight and Jia Zhao · 2020
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Transfer learning enhanced physics informed neural network for phase-field modeling of fracture
Somdatta Goswami, Cosmin Anitescu, Souvik Chakraborty, and Timon Rabczuk · 2020
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Gradient surgery for multi-task learning
Tianhe Yu, Saurabh Kumar, Abhishek Gupta, Sergey Levine, Karol Hausman, and Chelsea Finn · 2020
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Scalable second order optimization for deep learning
Rohan Anil, Vineet Gupta, Tomer Koren, Kevin Regan, and Yoram Singer · 2020
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Fourier features let networks learn high frequency functions in low dimensional domains
Matthew Tancik, Pratul P Srinivasan, Ben Mildenhall, Sara Fridovich-Keil, Nithin Raghavan, Utkarsh Singhal, Ravi Ramamoorthi, Jonathan T Barron, and Ren Ng · 2020
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Self-adaptive physics-informed neural networks using a soft attention mechanism
Levi McClenny and Ulisses Braga-Neto · 2020
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Understanding and mitigating gradient flow pathologies in physics-informed neural networks
Sifan Wang, Yujun Teng, and Paris Perdikaris · 2021
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Multiplicative filter networks
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Ben Moseley, Andrew Markham, and Tarje Nissen-Meyer · 2021
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On the eigenvector bias of fourier feature networks: From regression to solving multi-scale PDEs with physics-informed neural networks
Sifan Wang, Hanwen Wang, and Paris Perdikaris · 2021
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Efficient training of physics-informed neural networks via importance sampling
Mohammad Amin Nabian, Rini Jasmine Gladstone, and Hadi Meidani · 2021
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Characterizing possible failure modes in physics-informed neural networks
Aditi S Krishnapriyan, Amir Gholami, Shandian Zhe, Robert M Kirby, and Michael W Mahoney · 2021
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One-shot transfer learning of physics-informed neural networks
Shaan Desai, Marios Mattheakis, Hayden Joy, Pavlos Protopapas, and Stephen Roberts · 2021
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Transfer learning based multi-fidelity physics informed deep neural network
Souvik Chakraborty · 2021
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hp-vpinns: Variational physics-informed neural networks with domain decomposition
Ehsan Kharazmi, Zhongqiang Zhang, and George Em Karniadakis · 2021
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Sobolev training for physics informed neural networks
Hwijae Son, Jin Woo Jang, Woo Jin Han, and Hyung Ju Hwang · 2021
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A method for representing periodic functions and enforcing exactly periodic boundary conditions with deep neural networks
Suchuan Dong and Naxian Ni · 2021
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Towards impartial multi-task learning
Liyang Liu, Yi Li, Zhanghui Kuang, J Xue, Yimin Chen, Wenming Yang, Qingmin Liao, and Wayne Zhang · 2021
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Tsonn: Time-stepping-oriented neural network for solving partial differential equations
Wenbo Cao and Weiwei Zhang · 2023
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An expert’s guide to training physics-informed neural networks
Sifan Wang, Shyam Sankaran, Hanwen Wang, and Paris Perdikaris · 2023
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Pinnacle: A comprehensive benchmark of physics-informed neural networks for solving pdes
Zhongkai Hao, Jiachen Yao, Chang Su, Hang Su, Ziao Wang, Fanzhi Lu, Zeyu Xia, Yichi Zhang, Songming Liu, Lu Lu, et al · 2023
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A theory on adam instability in large-scale machine learning
Igor Molybog, Peter Albert, Moya Chen, Zachary DeVito, David Esiobu, Naman Goyal, Punit Singh Koura, Sharan Narang, Andrew Poulton, Ruan Silva, et al · 2023
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Convergence and dynamical behavior of the adam algorithm for nonconvex stochastic optimization
Anas Barakat and Pascal Bianchi · 2021
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A deeper look at the hessian eigenspectrum of deep neural networks and its applications to regularization
Adepu Ravi Sankar, Yash Khasbage, Rahul Vigneswaran, and Vineeth N Balasubramanian · 2021
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Prediction of porous media fluid flow using physics informed neural networks
Muhammad M Almajid and Moataz O Abu-Al-Saud · 2022
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Physics-informed neural networks for solving reynolds-averaged navier–stokes equations
Hamidreza Eivazi, Mojtaba Tahani, Philipp Schlatter, and Ricardo Vinuesa · 2022
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On the application of physics informed neural networks (pinn) to solve boundary layer thermal-fluid problems
Hassan Bararnia and Mehdi Esmaeilpour · 2022
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Physics informed neural networks for control oriented thermal modeling of buildings
Gargya Gokhale, Bert Claessens, and Chris Develder · 2022
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Analyses of internal structures and defects in materials using physics-informed neural networks
Enrui Zhang, Ming Dao, George Em Karniadakis, and Subra Suresh · 2022
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Sokratis J Anagnostopoulos, Juan Diego Toscano, Nikolaos Stergiopulos, and George Em Karniadakis · 2023
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About optimal loss function for training physics-informed neural networks under respecting causality
Vasiliy A Es’ kin, Danil V Davydov, Ekaterina D Egorova, Alexey O Malkhanov, Mikhail A Akhukov, and Mikhail E Smorkalov · 2023
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Soap: Improving and stabilizing shampoo using adam
Nikhil Vyas, Depen Morwani, Rosie Zhao, Itai Shapira, David Brandfonbrener, Lucas Janson, and Sham Kakade · 2024
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Surrogate modeling of multi-dimensional premixed and non-premixed combustion using pseudo-time stepping physics-informed neural networks
Zhen Cao, Kai Liu, Kun Luo, Sifan Wang, Liang Jiang, and Jianren Fan · 2024
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Physics-informed neural network estimation of material properties in soft tissue nonlinear biomechanical models
Federica Caforio, Francesco Regazzoni, Stefano Pagani, Elias Karabelas, Christoph Augustin, Gundolf Haase, Gernot Plank, and Alfio Quarteroni · 2024
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Physics-informed neural networks (pinn) for computational solid mechanics: Numerical frameworks and applications
Haoteng Hu, Lehua Qi, and Xujiang Chao · 2024
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Seismicnet: Physics-informed neural networks for seismic wave modeling in semi-infinite domain
Pu Ren, Chengping Rao, Su Chen, Jian-Xun Wang, Hao Sun, and Yang Liu · 2024
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Separable physics-informed neural networks
Junwoo Cho, Seungtae Nam, Hyunmo Yang, Seok-Bae Yun, Youngjoon Hong, and Eunbyung Park · 2024
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Piratenets: Physics-informed deep learning with residual adaptive networks
Sifan Wang, Bowen Li, Yuhan Chen, and Paris Perdikaris · 2024
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Physical activation functions (pafs): An approach for more efficient induction of physics into physics-informed neural networks (pinns)
Jassem Abbasi and Pål Østebø Andersen · 2024
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δ \delta -pinns: physics-informed neural networks on complex geometries
Francisco Sahli Costabal, Simone Pezzuto, and Paris Perdikaris · 2024
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Rbf-pinn: Non-fourier positional embedding in physics-informed neural networks
Chengxi Zeng, Tilo Burghardt, and Alberto M Gambaruto · 2024
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Efficient physics-informed neural networks using hash encoding
Xinquan Huang and Tariq Alkhalifah · 2024
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Gauss-newton natural gradient descent for physics-informed computational fluid dynamics
Anas Jnini, Flavio Vella, and Marius Zeinhofer · 2024
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The admm-pinns algorithmic framework for nonsmooth pde-constrained optimization: a deep learning approach
Yongcun Song, Xiaoming Yuan, and Hangrui Yue · 2024
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Wenqian Chen, Amanda A Howard, and Panos Stinis · 2024
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Residual-based attention in physics-informed neural networks
Sokratis J Anagnostopoulos, Juan Diego Toscano, Nikolaos Stergiopulos, and George Em Karniadakis · 2024
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Discontinuity computing using physics-informed neural networks
Li Liu, Shengping Liu, Hui Xie, Fansheng Xiong, Tengchao Yu, Mengjuan Xiao, Lufeng Liu, and Heng Yong · 2024
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Config: Towards conflict-free training of physics informed neural networks
Qiang Liu, Mengyu Chu, and Nils Thuerey · 2024
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Dual cone gradient descent for training physics-informed neural networks
Youngsik Hwang and Dongyoung Lim · 2024
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Muon: An optimizer for hidden layers in neural networks, 2024
Keller Jordan, Yuchen Jin, Vlado Boza, Jiacheng You, Franz Cesista, Laker Newhouse, and Jeremy Bernstein · 2024
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Challenges in training pinns: A loss landscape perspective
Pratik Rathore, Weimu Lei, Zachary Frangella, Lu Lu, and Madeleine Udell · 2024
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On the dynamics of three-layer neural networks: initial condensation
Zheng-an Chen and Tao Luo · 2024
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A new perspective on shampoo’s preconditioner
Depen Morwani, Itai Shapira, Nikhil Vyas, Eran Malach, Sham Kakade, and Lucas Janson · 2024
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Room impulse response reconstruction with physics-informed deep learning
Xenofon Karakonstantis, Diego Caviedes-Nozal, Antoine Richard, and Efren Fernandez-Grande · 2024
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IncompressibleNavierStokes.jl, November 2024
Syver Døving Agdestein, Simone Ciarella, and Benjamin Sanderse · 2024
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Unveiling the optimization process of physics informed neural networks: How accurate and competitive can pinns be?
Jorge F Urbán, Petros Stefanou, and José A Pons · 2025
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Vw-pinns: A volume weighting method for pde residuals in physics-informed neural networks
Jiahao Song, Wenbo Cao, Fei Liao, and Weiwei Zhang · 2025
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