About

Dr. Tan Bui-Thanh is a professor and the endowed William J. Murray Jr. Fellow in Engineering No. 4 in the Department of Aerospace Engineering and Engineering Mechanics (ASE/EM) and the Oden Institute for Computational Engineering and Sciences at The University of Texas at Austin. He obtained his Ph.D. from the Massachusetts Institute of Technology in 2007. Since joining the ASE/EM department in 2013, he has developed extensive expertise in multidisciplinary research across the boundaries of different branches of computational science, engineering, and mathematics. His research interests include quantum-accelerated Scientific Machine Learning (SciML) algorithms for digital twins, model-constrained Scientific Deep Learning (SciDL) algorithms, inverse problems, uncertainty quantification, numerical analysis, numerical optimization, and reduced-order modeling. Dr. Bui-Thanh has contributed significantly to PDE-constrained inverse problems, Bayesian inverse problems, and high-order finite element methods, and has developed physics-aware SciML approaches for computational sciences, engineering, and mathematics. He has published numerous works on real-time forecast and calibration (inversion) SciML algorithms that are deployable for digital twin applications, and is currently working on quantum-accelerated SciML algorithms for digital twins. He is a co-director of the Center for Scientific Machine Learning at the Oden Institute and has held leadership roles such as vice president of the SIAM Texas-Louisiana Section and secretary of the SIAM SIAG/CSE. Dr. Bui-Thanh has received several awards, including the NSF CAREER award, the Oden Institute distinguished research award, the Moncrief Grand Challenge award (twice), and was a Gordon Bell Prize finalist. His work is characterized by a focus on advancing computational methods for scientific and engineering problems, with particular emphasis on real-time applications and digital twin technologies.

Selected publications

• Variance-Reduced Diffusion Sampling via Target Score Identity

  ArXiv.org · 2026-01-04

  articleOpen accessSenior author

  We study variance reduction for score estimation and diffusion-based sampling in settings where the clean (target) score is available or can be approximated. Starting from the Target Score Identity (TSI), which expresses the noisy marginal score as a conditional expectation of the target score under the forward diffusion, we develop: (i) a plug-and-play nonparametric self-normalized importance sampling estimator compatible with standard reverse-time solvers, (ii) a variance-minimizing \emph{state- and time-dependent} blending rule between Tweedie-type and TSI estimators together with an anti-correlation analysis, (iii) a data-only extension based on locally fitted proxy scores, and (iv) a likelihood-tilting extension to Bayesian inverse problems. We also propose a \emph{Critic--Gate} distillation scheme that amortizes the state-dependent blending coefficient into a neural gate. Experiments on synthetic targets and PDE-governed inverse problems demonstrate improved sample quality for a fixed simulation budget.

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• Variance-Reduced Diffusion Sampling via Target Score Identity

  arXiv (Cornell University) · 2026-01-04

  preprintOpen accessSenior author

  We study variance reduction for score estimation and diffusion-based sampling in settings where the clean (target) score is available or can be approximated. Starting from the Target Score Identity (TSI), which expresses the noisy marginal score as a conditional expectation of the target score under the forward diffusion, we develop: (i) a plug-and-play nonparametric self-normalized importance sampling estimator compatible with standard reverse-time solvers, (ii) a variance-minimizing \emph{state- and time-dependent} blending rule between Tweedie-type and TSI estimators together with an anti-correlation analysis, (iii) a data-only extension based on locally fitted proxy scores, and (iv) a likelihood-tilting extension to Bayesian inverse problems. We also propose a \emph{Critic--Gate} distillation scheme that amortizes the state-dependent blending coefficient into a neural gate. Experiments on synthetic targets and PDE-governed inverse problems demonstrate improved sample quality for a fixed simulation budget.

  PublisherDOI

• The AI Research Assistant: Promise, Peril, and a Proof of Concept

  Computing in Science & Engineering · 2026-01-01

  article1st authorCorresponding

  Can artificial intelligence truly contribute to creative mathematical research, or does it merely automate routine calculations while introducing risks of error? We provide empirical evidence through a detailed case study: the discovery of novel error representations and bounds for Hermite quadrature rules via systematic human-AI collaboration. <p xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Working with multiple AI assistants, we extended results beyond what manual work achieved, formulating and proving several theorems with AI assistance. The collaboration revealed both remarkable capabilities and critical limitations. AI excelled at algebraic manipulation, systematic proof exploration, literature synthesis, and LaTeX preparation. However, every step required rigorous human verification, mathematical intuition for problem formulation, and strategic direction. We document the complete research workflow with unusual transparency, revealing patterns in successful human-AI mathematical collaboration and identifying failure modes researchers must anticipate. Our experience suggests that, when used with appropriate skepticism and verification protocols, AI tools can meaningfully accelerate mathematical discovery while demanding careful human oversight and deep domain expertise.

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• LiLaN: A Linear Latent Network as the Solution Operator for Real-Time Solutions to Stiff Nonlinear Ordinary Differential Equations

  ArXiv.org · 2025-01-14

  preprintOpen access

  Solving stiff ordinary differential equations (StODEs) requires sophisticated numerical solvers, which are often computationally expensive. In general, traditional explicit time integration schemes with restricted time step sizes are not suitable for StODEs, and one must resort to costly implicit methods. On the other hand, state-of-the-art machine learning based methods, such as Neural ODE, poorly handle the timescale separation of various elements of the solutions to StODEs, while still requiring expensive implicit/explicit integration at inference time. In this work, we propose a linear latent network (LiLaN) approach in which the dynamics in the latent space can be integrated analytically, and thus numerical integration is completely avoided. At the heart of LiLaN are the following key ideas: i) two encoder networks to encode the initial condition together with parameters of the ODE to the slope and the initial condition for the latent dynamics, respectively. Since the latent dynamics, by design, are linear, the solution can be evaluated analytically; ii) a neural network to map the physical time to latent times, one for each latent variable. Finally, iii) a decoder network to decode the latent solution to the physical solution at the corresponding physical time. We provide a universal approximation theorem for the proposed LiLaN approach, showing that it can approximate the solution of any stiff nonlinear system on a compact set to any degree of accuracy epsilon. We also show an interesting fact that the dimension of the latent dynamical system in LiLaN is independent of epsilon. Numerical results on the "Robertson Stiff Chemical Kinetics Model," "Plasma Collisional-Radiative Model," and "Allen-Cahn" and "Cahn-Hilliard" PDEs suggest that LiLaN outperformed state-of-the-art machine learning approaches for handling stiff ordinary and partial differential equations.

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• A model-constrained discontinuous Galerkin Network (DGNet) for compressible Euler equations with out-of-distribution generalization

  Computer Methods in Applied Mechanics and Engineering · 2025-03-30 · 1 citations

  articleOpen accessSenior author

  Real-time accurate solutions of large-scale complex dynamical systems are critically needed for control, optimization, uncertainty quantification , and decision-making in practical engineering and science applications, particularly in digital twin contexts. Recent research on hybrid approaches combining numerical methods and machine learning in end-to-end training has shown significant improvements over either approach alone. However, using neural networks as surrogate models generally exhibits limitations in generalizability over different settings and in capturing the evolution of solution discontinuities. In this work, we develop a model-constrained discontinuous Galerkin Network ( DGNet ) approach, a significant extension to our previous work (Nguyen and Bui-Thanh, 2022), for compressible Euler equations with out-of-distribution generalization. The core of DGNet is the synergy of several key strategies: (i) leveraging time integration schemes to capture temporal correlation and taking advantage of neural network speed for computation time reduction. This is the key to the temporal discretization-invariant property of DGNet ; (ii) employing a model-constrained approach to ensure the learned tangent slope satisfies governing equations; (iii) utilizing a DG-inspired architecture for GNN where edges represent Riemann solver surrogate models and nodes represent volume integration correction surrogate models, enabling capturing discontinuity capability, aliasing error reduction, and mesh discretization generalizability. Such a design allows DGNet to learn the DG spatial discretization accurately; (iv) developing an input normalization strategy that allows surrogate models to generalize across different initial conditions, geometries, meshes, boundary conditions, and solution orders. In fact, the normalization is the key to spatial discretization-invariance for DGNet ; and (v) incorporating a data randomization technique that not only implicitly promotes agreement between surrogate models and true numerical models up to second-order derivatives, ensuring long-term stability and prediction capacity, but also serves as a data generation engine during training, leading to enhanced generalization on unseen data. To validate the theoretical results, effectiveness, stability, and generalizability of our novel DGNet approach, we present comprehensive numerical results for 1D and 2D compressible Euler equation problems, including Sod Shock Tube , Lax Shock Tube, Isentropic Vortex, Forward Facing Step, Scramjet, Airfoil , Euler Benchmarks, Double Mach Reflection, and a Hypersonic Sphere Cone benchmark.

  PublisherDOI

• An adaptive and stability-promoting layerwise training approach for sparse deep neural network architecture

  Computer Methods in Applied Mechanics and Engineering · 2025-04-03 · 1 citations

  articleOpen accessSenior author

  This work presents a two-stage adaptive framework for progressively developing deep neural network (DNN) architectures that generalize well for a given training data set. In the first stage, a layerwise training approach is adopted where a new layer is added each time and trained independently by freezing parameters in the previous layers. We impose desirable structures on the DNN by employing manifold regularization, sparsity regularization, and physics-informed terms. We introduce a ε – δ – stability-promoting concept as a desirable property for a learning algorithm and show that employing manifold regularization yields a ε – δ stability-promoting algorithm. Further, we also derive the necessary conditions for the trainability of a newly added layer and investigate the training saturation problem. In the second stage of the algorithm (post-processing), a sequence of shallow networks is employed to extract information from the residual produced in the first stage, thereby improving the prediction accuracy. Numerical investigations on prototype regression and classification problems demonstrate that the proposed approach can outperform fully connected DNNs of the same size. Moreover, by equipping the physics-informed neural network (PINN) with the proposed adaptive architecture strategy to solve partial differential equations, we numerically show that adaptive PINNs not only are superior to standard PINNs but also produce interpretable hidden layers with provable stability. As a result, we also apply our architecture design strategy to solve inverse problems governed by elliptic partial differential equations.

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• Improvements on uncertainty quantification with variational autoencoders

  ArXiv.org · 2025-09-14

  preprintOpen access

  Inverse problems aim to determine model parameters of a mathematical problem from given observational data. Neural networks can provide an efficient tool to solve these problems. In the context of Bayesian inverse problems, Uncertainty Quantification Variational AutoEncoders (UQ-VAE), a class of neural networks, approximate the posterior distribution mean and covariance of model parameters. This allows for both the estimation of the parameters and their uncertainty in relation to the observational data. In this work, we propose a novel loss function for training UQ-VAEs, which includes, among other modifications, the removal of a sample mean term from an already existing one. This modification improves the accuracy of UQ-VAEs, as the original theoretical result relies on the convergence of the sample mean to the expected value (a condition that, in high dimensional parameter spaces, requires a prohibitively large number of samples due to the curse of dimensionality). Avoiding the computation of the sample mean significantly reduces the training time in high dimensional parameter spaces compared to previous literature results. Under this new formulation, we establish a new theoretical result for the approximation of the posterior mean and covariance for general mathematical problems. We validate the effectiveness of UQ-VAEs through three benchmark numerical tests: a Poisson inverse problem, a non affine inverse problem and a 0D cardiocirculatory model, under the two clinical scenarios of systemic hypertension and ventricular septal defect. For the latter case, we perform forward uncertainty quantification.

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• Taen: A Model-Constrained Tikhonov Autoencoder Network for Forward and Inverse Problems

  SSRN Electronic Journal · 2025-01-01

  preprintOpen access
  PublisherDOI

• Use of mobile phone sensing data to estimate residence and occupation times in urban patches: human mobility restrictions and the 2020 COVID-19 outbreak in Hermosillo, Mexico

  Computational Urban Science · 2025-02-25 · 3 citations

  articleOpen accessSenior author

  Abstract Understanding the impact of population mobility on the spread of infectious diseases is crucial for designing effective interventions. Traditional models, such as origin-destination matrices, often lack the spatial and temporal resolution needed to accurately capture these dynamics. This study addresses this gap by introducing a novel methodology to estimate time-varying occupancy patterns across urban zones (patches) using geospatial data from mobile phones. By leveraging Brownian bridge models at an inhabitant-patch level, we construct a residence-occupation matrix (ROM) that represents the fraction of time individuals spend in each urban patch. We apply this approach to real-world data from Hermosillo, Sonora, Mexico, during the COVID-19 pandemic. Our findings show that even small shifts in local mobility patterns can significantly alter the epidemic’s trajectory, highlighting the importance of high-resolution mobility data in modeling infectious disease spread. These changes can be patch-specific, and their contribution to the overall evolution depends on the mobility dynamics and population sizes within each patch. The proposed ROM serves as a key input for multi-patch epidemiological models, that in turn, can provide more realistic epidemic forecasts, facilitating the evaluation of the effectiveness of patch-specific and global mobility restrictions, and improving the estimation of epidemiological parameters of such models in related research. Additionally, the ROM framework can be adapted to other patch-based models modeling various phenomena influenced by human mobility.

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• Topological derivative approach for deep neural network architecture adaptation

  ArXiv.org · 2025-02-08

  preprintOpen access

  This work presents a novel algorithm for progressively adapting neural network architecture along the depth. In particular, we attempt to address the following questions in a mathematically principled way: i) Where to add a new capacity (layer) during the training process? ii) How to initialize the new capacity? At the heart of our approach are two key ingredients: i) the introduction of a ``shape functional" to be minimized, which depends on neural network topology, and ii) the introduction of a topological derivative of the shape functional with respect to the neural network topology. Using an optimal control viewpoint, we show that the network topological derivative exists under certain conditions, and its closed-form expression is derived. In particular, we explore, for the first time, the connection between the topological derivative from a topology optimization framework with the Hamiltonian from optimal control theory. Further, we show that the optimality condition for the shape functional leads to an eigenvalue problem for deep neural architecture adaptation. Our approach thus determines the most sensitive location along the depth where a new layer needs to be inserted during the training phase and the associated parametric initialization for the newly added layer. We also demonstrate that our layer insertion strategy can be derived from an optimal transport viewpoint as a solution to maximizing a topological derivative in $p$-Wasserstein space, where $p&gt;= 1$. Numerical investigations with fully connected network, convolutional neural network, and vision transformer on various regression and classification problems demonstrate that our proposed approach can outperform an ad-hoc baseline network and other architecture adaptation strategies. Further, we also demonstrate other applications of topological derivative in fields such as transfer learning.

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Awards & honors

• William J Murray Jr. Fellow in Engineering No. 4
• NSF (OAC/DMS) early CAREER award
• Oden Institute distinguished research award
• Moncrief Grand Challenge award (two-time winner)
• Gordon Bell Prize finalist