182 citations · 462 across the 20 of their papers we have counts for
22 papers
Cost-Accuracy Trade-offs: Neural Operator vs Classical Numerical Solver
Daniel Zhengyu Huang, Andrew M. Stuart
Neural operators are data-driven models that learn mappings from inputs that parameterize partial differential equations, such as spatially varying coefficients, initial conditions…
AI-aided Geometric Design of Anti-infection Catheters
Tingtao Zhou, Xuan Wan, Daniel Zhengyu Huang +6
Bacteria can swim upstream due to hydrodynamic interactions with the fluid flow in a narrow tube, and pose a clinical threat of urinary tract infection to patients implanted with c…
Gradient Flows for Sampling: Mean-Field Models, Gaussian Approximations and Affine Invariance
Yifan Chen, Daniel Zhengyu Huang, Jiaoyang Huang +2
Sampling a probability distribution with an unknown normalization constant is a fundamental problem in computational science and engineering. This task may be cast as an optimizati…
Bayesian Spline Learning for Equation Discovery of Nonlinear Dynamics with Quantified Uncertainty
Luning Sun, Daniel Zhengyu Huang, Hao Sun +1
Nonlinear dynamics are ubiquitous in science and engineering applications, but the physics of most complex systems is far from being fully understood. Discovering interpretable gov…
Fourier Neural Operator with Learned Deformations for PDEs on General Geometries
Zongyi Li, Daniel Zhengyu Huang, Burigede Liu +1
Deep learning surrogate models have shown promise in solving partial differential equations (PDEs). Among them, the Fourier neural operator (FNO) achieves good accuracy, and is sig…
Efficient Derivative-free Bayesian Inference for Large-Scale Inverse Problems
Daniel Zhengyu Huang, Jiaoyang Huang, Sebastian Reich +1
We consider Bayesian inference for large scale inverse problems, where computational challenges arise from the need for repeated evaluations of an expensive forward model. This ren…
The Cost-Accuracy Trade-Off In Operator Learning With Neural Networks
Maarten V. de Hoop, Daniel Zhengyu Huang, Elizabeth Qian +1
The term `surrogate modeling' in computational science and engineering refers to the development of computationally efficient approximations for expensive simulations, such as thos…
Long Random Matrices and Tensor Unfolding
Gérard Ben Arous, Daniel Zhengyu Huang, Jiaoyang Huang
In this paper, we consider the singular values and singular vectors of low rank perturbations of large rectangular random matrices, in the regime the matrix is "long": we allow the…
Bayesian Calibration for Large-Scale Fluid Structure Interaction Problems Under Embedded/Immersed Boundary Framework
Shunxiang Cao, Daniel Zhengyu Huang
Bayesian calibration is widely used for inverse analysis and uncertainty analysis for complex systems in the presence of both computer models and observation data. In the present w…
Unscented Kalman Inversion: Efficient Gaussian Approximation to the Posterior Distribution
Daniel Z. Huang, Jiaoyang Huang
The unscented Kalman inversion (UKI) method presented in [1] is a general derivative-free approach for the inverse problem. UKI is particularly suitable for inverse problems where…
Improve Unscented Kalman Inversion With Low-Rank Approximation and Reduced-Order Model
Daniel Z. Huang, Jiaoyang Huang
The unscented Kalman inversion (UKI) presented in [1] is a general derivative-free approach to solving the inverse problem. UKI is particularly suitable for inverse problems where…
Iterated Kalman Methodology For Inverse Problems
Daniel Zhengyu Huang, Tapio Schneider, Andrew M. Stuart
This paper is focused on the optimization approach to the solution of inverse problems. We introduce a stochastic dynamical system in which the parameter-to-data map is embedded, w…
Power Iteration for Tensor PCA
Jiaoyang Huang, Daniel Z. Huang, Qing Yang +1
In this paper, we study the power iteration algorithm for the spiked tensor model, as introduced in [44]. We give necessary and sufficient conditions for the convergence of the pow…
A Computationally Tractable Framework for Nonlinear Dynamic Multiscale Modeling of Membrane Fabric
Philip Avery, Daniel Z. Huang, Wanli He +3
A general-purpose computational homogenization framework is proposed for the nonlinear dynamic analysis of membranes exhibiting complex microscale and/or mesoscale heterogeneity ch…
Learning Constitutive Relations using Symmetric Positive Definite Neural Networks
Kailai Xu, Daniel Z. Huang, Eric Darve
We present the Cholesky-factored symmetric positive definite neural network (SPD-NN) for modeling constitutive relations in dynamical equations. Instead of directly predicting the…
Modeling, simulation and validation of supersonic parachute inflation dynamics during Mars landing
Daniel Z. Huang, Philip Avery, Charbel Farhat +3
A high fidelity multi-physics Eulerian computational framework is presented for the simulation of supersonic parachute inflation during Mars landing. Unlike previous investigations…
High-order partitioned spectral deferred correction solvers for multiphysics problems
Daniel Z. Huang, Will Pazner, Per-Olof Persson +1
We present an arbitrarily high-order, conditionally stable, partitioned spectral deferred correction (SDC) method for solving multiphysics problems using a sequence of pre-existing…
An Embedded Boundary Approach for Resolving the Contribution of Cable Subsystems to Fully Coupled Fluid-Structure Interaction
Daniel Z. Huang, Philip Avery, Charbel Farhat
Cable subsystems characterized by long, slender, and flexible structural elements are featured in numerous engineering systems. In each of them, interaction between an individual c…
Homogenized Flux-Body Force Treatment of Compressible Viscous Porous Wall Boundary Conditions
Daniel Z. Huang, Man Long Wong, Sanjiva K. Lele +1
A homogenization approach is proposed for the treatment of porous wall boundary conditions in the computation of compressible viscous flows. Like any other homogenization approach,…
Learning Constitutive Relations from Indirect Observations Using Deep Neural Networks
Daniel Z. Huang, Kailai Xu, Charbel Farhat +1
We present a new approach for predictive modeling and its uncertainty quantification for mechanical systems, where coarse-grained models such as constitutive relations are derived…
A high-order partitioned solver for general multiphysics problems and its applications in optimization
Daniel Z. Huang, Per-Olof Persson, Matthew J. Zahr
A high-order accurate adjoint-based optimization framework is presented for unsteady multiphysics problems. The fully discrete adjoint solver relies on the high-order, linearly sta…
High-order, linearly stable, partitioned solvers for general multiphysics problems based on implicit-explicit Runge-Kutta schemes
Daniel Z. Huang, Per-Olof Persson, Matthew J. Zahr
This work introduces a general framework for constructing high-order, linearly stable, partitioned solvers for multiphysics problems from a monolithic implicit-explicit Runge-Kutta…