166 citations · 397 across the 11 of their papers we have counts for
9 papers · 1 filter
Stochastic Taylor Derivative Estimator: Efficient amortization for arbitrary differential operators
Zekun Shi, Zheyuan Hu, Min Lin +1
Optimizing neural networks with loss that contain high-dimensional and high-order differential operators is expensive to evaluate with back-propagation due to …
State-space models are accurate and efficient neural operators for dynamical systems
Zheyuan Hu, Nazanin Ahmadi Daryakenari, Qianli Shen +2
Physics-informed machine learning (PIML) has emerged as a promising alternative to classical methods for predicting dynamical systems, offering faster and more generalizable soluti…
Score-fPINN: Fractional Score-Based Physics-Informed Neural Networks for High-Dimensional Fokker-Planck-Levy Equations
Zheyuan Hu, Zhongqiang Zhang, George Em Karniadakis +1
We introduce an innovative approach for solving high-dimensional Fokker-Planck-Lévy (FPL) equations in modeling non-Brownian processes across disciplines such as physics, finance,…
Score-Based Physics-Informed Neural Networks for High-Dimensional Fokker-Planck Equations
Zheyuan Hu, Zhongqiang Zhang, George Em Karniadakis +1
The Fokker-Planck (FP) equation is a foundational PDE in stochastic processes. However, curse of dimensionality (CoD) poses challenge when dealing with high-dimensional FP PDEs. Al…
Hutchinson Trace Estimation for High-Dimensional and High-Order Physics-Informed Neural Networks
Zheyuan Hu, Zekun Shi, George Em Karniadakis +1
Physics-Informed Neural Networks (PINNs) have proven effective in solving partial differential equations (PDEs), especially when some data are available by seamlessly blending data…
Bias-Variance Trade-off in Physics-Informed Neural Networks with Randomized Smoothing for High-Dimensional PDEs
Zheyuan Hu, Zhouhao Yang, Yezhen Wang +2
While physics-informed neural networks (PINNs) have been proven effective for low-dimensional partial differential equations (PDEs), the computational cost remains a hurdle in high…
Tackling the Curse of Dimensionality with Physics-Informed Neural Networks
Zheyuan Hu, Khemraj Shukla, George Em Karniadakis +1
The curse-of-dimensionality taxes computational resources heavily with exponentially increasing computational cost as the dimension increases. This poses great challenges in solvin…
D4FT: A Deep Learning Approach to Kohn-Sham Density Functional Theory
Tianbo Li, Min Lin, Zheyuan Hu +6
Kohn-Sham Density Functional Theory (KS-DFT) has been traditionally solved by the Self-Consistent Field (SCF) method. Behind the SCF loop is the physics intuition of solving a syst…
Augmented Physics-Informed Neural Networks (APINNs): A gating network-based soft domain decomposition methodology
Zheyuan Hu, Ameya D. Jagtap, George Em Karniadakis +1
In this paper, we propose the augmented physics-informed neural network (APINN), which adopts soft and trainable domain decomposition and flexible parameter sharing to further impr…