Publications (12)
Deep Gaussian Processes for Functional Maps
Matthew Lowery, Zhitong Xu, Da Long +5
Learning mappings between functional spaces, also known as function-on-function regression, is a fundamental problem in functional data analysis with broad applications, including…
Pseudo-Physics-Informed Neural Operators: Enhancing Operator Learning from Limited Data
Keyan Chen, Yile Li, Da Long +4
Neural operators have shown great potential in surrogate modeling. However, training a well-performing neural operator typically requires a substantial amount of data, which can po…
Arbitrarily-Conditioned Multi-Functional Diffusion for Multi-Physics Emulation
Da Long, Zhitong Xu, Guang Yang +2
Modern physics simulation often involves multiple functions of interests, and traditional numerical approaches are known to be complex and computationally costly. While machine lea…
Deep peak property learning for efficient chiral molecules ECD spectra prediction
Hao Li, Da Long, Li Yuan +3
Chiral molecule assignation is crucial for asymmetric catalysis, functional materials, and the drug industry. The conventional approach requires theoretical calculations of electro…
Equation Discovery with Bayesian Spike-and-Slab Priors and Efficient Kernels
Da Long, Wei W. Xing, Aditi S. Krishnapriyan +3
Discovering governing equations from data is important to many scientific and engineering applications. Despite promising successes, existing methods are still challenged by data s…
AutoIP: A United Framework to Integrate Physics into Gaussian Processes
Da Long, Zheng Wang, Aditi Krishnapriyan +3
Physical modeling is critical for many modern science and engineering applications. From a data science or machine learning perspective, where more domain-agnostic, data-driven mod…
Dual-Agent Co-Training for Health Coaching via Implicit Adversarial Preference Optimization
Da Long, Lingyi Fu, Diya Michelle Rao +3
Motivational-interviewing-based health coaching is an effective approach for improving mental health and promoting healthy behavior change. However, the scarcity of trained human c…
Toward Efficient Kernel-Based Solvers for Nonlinear PDEs
Zhitong Xu, Da Long, Yiming Xu +3
We introduce a novel kernel learning framework toward efficiently solving nonlinear partial differential equations (PDEs). In contrast to the state-of-the-art kernel solver that em…
Solving High Frequency and Multi-Scale PDEs with Gaussian Processes
Shikai Fang, Madison Cooley, Da Long +3
Machine learning based solvers have garnered much attention in physical simulation and scientific computing, with a prominent example, physics-informed neural networks (PINNs). How…
Invertible Fourier Neural Operators for Tackling Both Forward and Inverse Problems
Da Long, Zhitong Xu, Qiwei Yuan +2
Fourier Neural Operator (FNO) is a powerful and popular operator learning method. However, FNO is mainly used in forward prediction, yet a great many applications rely on solving i…
StFT: Spatio-temporal Fourier Transformer for Long-term Dynamics Prediction
Da Long, Shandian Zhe, Samuel Williams +2
Simulating the long-term dynamics of multi-scale and multi-physics systems poses a significant challenge in understanding complex phenomena across science and engineering. The comp…
A Kernel Approach for PDE Discovery and Operator Learning
Da Long, Nicole Mrvaljevic, Shandian Zhe +1
This article presents a three-step framework for learning and solving partial differential equations (PDEs) using kernel methods. Given a training set consisting of pairs of noisy…