arXiv subjects

Youngsoo Choi

Publications and source records attributed to Youngsoo Choi.

At least 19 recordsLinked to original sources

arXiv2026

Online Spectral Deflation for State Constrained Optimal Control Problems

Parametric PDE-constrained optimal control with pointwise state constraints requires repeated solution of restricted Schur-complement systems on parameter-dependent inactive sets. In a primal active-set method, each inactive-set system is symmetric positive definite, but the active set can change nonsmoothly with the parameter. The resulting operator may vary in dimension, sparsity pattern, and spectrum, limiting reuse of sparse factorizations, multigrid hierarchies, and Krylov information. We propose a reusable spectral-deflation strategy anchored to one full-domain reference Schur complement. Low reference eigenmodes are computed once, restricted online to each inactive set, and used as an A-DEF2 deflation basis for Jacobi-preconditioned CG. The framework also supports POD enrichment, Rayleigh-Ritz reselection, coarse-grid or analytical reference modes, and conditioning safeguards. Given the active set, the method preserves the high-fidelity inactive-set system and solves it to the prescribed CG tolerance; it accelerates the linear algebra rather than replacing the optimal-control solve with a surrogate. We explain the method through a spectral-coherence view, motivated by interlacing and perturbation arguments and assessed with principal-angle diagnostics. Across diffusion, convection-diffusion, nonlinear thermal, and conjugate-heat-transfer benchmarks, deflation reduces CG iterations by about 55 to 98 percent. GPU deployments also show wall-time gains over CPU sparse-direct and algebraic-multigrid baselines, because the reference basis is built once whereas competing solver structures are rebuilt per instance. Coarse-grid or analytical modes amortize the offline cost within a single parameter sweep; fine-grid eigensolves remain more precompute-limited. Timings isolate the inactive-set linear-solve kernel; reducing the active-set outer loop is outside the present scope.

cs.CE↗

arXiv2026

Time-Dependent PDE-Constrained Optimization via Weak-Form Latent Dynamics

Optimization problems constrained by high-dimensional, time-dependent partial differential equations require repeated forward and sensitivity solves, making high-fidelity optimization computationally prohibitive in many-query design and control settings. We present a weak-form latent-space reduced-order modeling framework for accelerating gradient-based PDE-constrained optimization. The proposed approach builds on Weak-form Latent Space Dynamics Identification (WLaSDI), which compresses high-dimensional solution trajectories into a low-dimensional latent representation and identifies parametric latent dynamics using weak-form system identification. By avoiding explicit numerical differentiation of training trajectories, the weak-form improves robustness to noisy data and yields more reliable surrogate dynamics for optimization. We formulate the resulting reduced PDE-constrained optimization problem and derive both direct-sensitivity and adjoint-based gradient expressions for the learned latent dynamics, enabling scalable gradient evaluation with respect to design parameters. The framework is demonstrated on three time-dependent benchmark problems: thermal radiative transfer for optimal hohlraum design, the two-stream instability Vlasov-Poisson system, and the inviscid Burgers equation. Across these examples, WLaSDI produces accurate optimal designs, remains robust under noisy training data, and delivers substantial computational savings, including speedups of up to five orders of magnitude relative to full-order optimization. These results demonstrate that weak-form latent dynamics provide an efficient and noise-robust surrogate foundation for gradient-based optimization of complex time-dependent PDE systems.

math.OC↗

arXiv2026

Physics-Informed Latent Space Dynamics Identification for Time-Dependent NLTE Atomic Kinetics

Non-local thermodynamic equilibrium (NLTE) calculations remain a major computational bottleneck in radiation--hydrodynamics, while most existing machine-learning surrogates treat NLTE as a static input--output mapping rather than a kinetic evolution problem. Here, we present a physics-informed Latent Space Dynamics Identification (pLaSDI) framework specifically designed for NLTE atomic kinetics, which captures the time-dependent atomic kinetics of non-equilibrium plasmas through an explicit reduced governing equation. To ensure the physical reliability of the reduced model, we impose physics-informed loss terms that enforce macroscopic consistency, dynamical stability, and convergence to the correct steady state during long-time integration. Applied to tin NLTE population data generated along hydrodynamically modeled temperature--density trajectories relevant to extreme ultraviolet (EUV) lithography plasmas, the model accurately reproduces charge-state evolution and mean charge state with errors below 2\%, achieves speedups of approximately $5\times10^{4}$--$10^{5}$, and remains stable outside the training trajectories by converging toward physically admissible states and the correct steady-state solution under fixed plasma conditions. These results show that careful physics-informed design of the latent dynamics, rather than data fitting alone, is essential for constructing fast, stable, and physically reliable extrapolative surrogates for time-dependent NLTE kinetics.

physics.plasm-ph↗

arXiv2026

WGFINNs: Weak formulation-based GENERIC formalism informed neural networks

Data-driven discovery of governing equations from noisy observations remains a fundamental challenge in scientific machine learning. While GENERIC formalism informed neural networks (GFINNs) provide a principled framework that enforces the laws of thermodynamics by construction, their reliance on strong-form loss formulations makes them highly sensitive to measurement noise. To address this limitation, we propose weak formulation-based GENERIC formalism informed neural networks (WGFINNs), which integrate the weak formulation of dynamical systems with the structure-preserving architecture of GFINNs. WGFINNs significantly enhance robustness to noisy data while retaining exact satisfaction of GENERIC degeneracy and symmetry conditions. We further incorporate a state-wise weighted loss and a residual-based attention mechanism to mitigate scale imbalance across state variables. Theoretical analysis contrasts quantitative differences between the strong-form and the weak-form estimators. Mainly, the strong-form estimator diverges as the time step decreases in the presence of noise, while the weak-form estimator can be accurate even with noisy data if test functions satisfy certain conditions. Numerical experiments demonstrate that WGFINNs consistently outperform GFINNs at varying noise levels, achieving more accurate predictions and reliable recovery of physical quantities.

cs.LG↗

arXiv2026

Hyper-reduction methods for accelerating nonlinear finite element simulations: open source implementation and reproducible benchmarks

Hyper-reduction methods have gained increasing attention for their potential to accelerate reduced order models for nonlinear systems, yet their comparative accuracy and computational efficiency are not well understood. Motivated by this gap, we evaluate a range of hyper-reduction techniques for nonlinear finite element models across benchmark problems of varying complexity, assessing the inevitable tradeoff between accuracy and speedup. More specifically, we consider interpolation methods based on the gappy proper orthogonal decomposition as well as the empirical quadrature procedure (EQP), and apply them to the hyper-reduction of problems in nonlinear diffusion, nonlinear elasticity and Lagrangian hydrodynamics. Our numerical results are generated using the open source libROM, Laghos and MFEM numerical libraries. Our findings reveal that the comparative performance between hyper-reduction methods depends on both the problem and the choice of time integration method. The EQP method generally achieves lower relative errors than interpolation methods and is more efficient in terms of quadrature point usage, resulting in a lower wall time for the nonlinear diffusion and elasticity problems. However, its online computational cost is observed to be relatively high for Lagrangian hydrodynamics problems. Conversely, interpolation methods exhibit greater variability, especially with respect to the use of different time integration methods in the Lagrangian hydrodynamics problems. The presented results underscore the need for problem specific method selection to balance accuracy and efficiency, while also offering useful guidance for future comparisons and refinements of hyper-reduction techniques.

cs.MS↗

arXiv2026

A Reduced Order Model approach for First-Principles Molecular Dynamics Computations

To leverage the redundancy between the electronic structure computed at each step of first-principles molecular dynamics, we present a data-driven modeling framework for Kohn-Sham Density Functional Theory that bypasses the explicit optimization of electronic wavefunctions. We sample a priori representative atomic configurations and construct a low-dimensional basis that efficiently approximates the electronic structure subspace. Subsequently, we employ this reduced basis in a direct solver for the electronic single particle density matrix, thereby enabling the efficient determination of ground state without iterative wavefunction optimization. We demonstrate the efficacy of our approach in a Born-Oppenheimer molecular dynamics of a water molecule, showing that the resulting simulations accurately reproduce key structural properties, such as bond lengths and bond angle, obtained from full first-principles molecular dynamics. This work highlights the potential of data-driven approaches to develop efficient electronic structure solvers for first-principles simulations.

math.NA↗

arXiv2026

Latent Space Element Method

How can we build surrogate solvers that train on small domains but scale to larger ones without intrusive access to PDE operators? Inspired by the Data-Driven Finite Element Method (DD-FEM) framework for modular data-driven solvers, we propose the Latent Space Element Method (LSEM), an element-based latent surrogate assembly approach in which a learned subdomain ("element") model can be tiled and coupled to form a larger computational domain. Each element is a LaSDI latent ODE surrogate trained from snapshots on a local patch, and neighboring elements are coupled through learned directional interaction terms in latent space, avoiding Schwarz iterations and interface residual evaluations. A smooth window-based blending reconstructs a global field from overlapping element predictions, yielding a scalable assembled latent dynamical system. Experiments on the 1D Burgers and Korteweg-de Vries equations show that LSEM maintains predictive accuracy while scaling to spatial domains larger than those seen in training. LSEM offers an interpretable and extensible route toward foundation-model surrogate solvers built from reusable local models.

math.DS↗

arXiv2025

Higher-Order LaSDI: Reduced Order Modeling with Multiple Time Derivatives

Solving complex partial differential equations is vital in the physical sciences, but often requires computationally expensive numerical methods. Reduced-order models (ROMs) address this by exploiting dimensionality reduction to create fast approximations. While modern ROMs can solve parameterized families of PDEs, their predictive power degrades over long time horizons. We address this by (1) introducing a flexible, high-order, yet inexpensive finite-difference scheme and (2) proposing a Rollout loss that trains ROMs to make accurate predictions over arbitrary time horizons. We demonstrate our approach on the 2D Burgers equation.

cs.LG↗

arXiv2025

Offline Maximizing Minimally Invasive Proper Orthogonal Decomposition for Reduced Order Modeling of $S_n$ Radiation Transport

Deterministic solutions to the Sn transport equation can be computationally expensive to calculate. Reduced Order Models (ROMs) provide an efficient means of approximating the Full Order Model (FOM) solution. We propose a novel approach for constructing ROMs of the Sn radiation transport equation, Offline Maximizing Minimally Invasive (OMMI) Proper Orthogonal Decomposition (POD). POD uses snapshot data to build a reduced basis, which is then used to project the FOM. Minimally Invasive POD leverages the sweep infrastructure within deterministic Sn transport solvers to construct the reduced linear system, even though the FOM linear system is never directly assembled. OMMI-POD extends Minimally Invasive POD by performing transport sweeps offline, thereby maximizing the potential speedup. It achieves this by generating a library of reduced systems from a training set, which is then interpolated in the online stage to provide a rapid approximate solution to the Sn transport equation. The model's performance is evaluated on a multigroup 2-D test problem, demonstrating low error and a 1600-fold speedup over the full order model.

math.NA↗

arXiv2025

Sequential decoder training for improved latent space dynamics identification

Accurate numerical solutions of partial differential equations are essential in many scientific fields but often require computationally expensive solvers, motivating reduced-order models (ROMs). Latent Space Dynamics Identification (LaSDI) is a data-driven ROM framework that combines autoencoders with equation discovery to learn interpretable latent dynamics. However, enforcing latent dynamics during training can compromise reconstruction accuracy of the model for simulation data. We introduce multi-stage LaSDI (mLaSDI), a framework that improves reconstruction and prediction accuracy by sequentially learning additional decoders to correct residual errors from previous stages. Applied to the 1D-1V Vlasov equation, mLaSDI consistently outperforms standard LaSDI, achieving lower prediction errors and reduced training time across a wide range of architectures.

cs.LG↗

arXiv2025

Reduced Order Modeling of Energetic Materials Using Physics-Aware Recurrent Convolutional Neural Networks in a Latent Space (LatentPARC)

Physics-aware deep learning (PADL) has gained popularity for use in complex spatiotemporal dynamics (field evolution) simulations, such as those that arise frequently in computational modeling of energetic materials (EM). Here, we show that the challenge PADL methods face while learning complex field evolution problems can be simplified and accelerated by decoupling it into two tasks: learning complex geometric features in evolving fields and modeling dynamics over these features in a lower dimensional feature space. To accomplish this, we build upon our previous work on physics-aware recurrent convolutions (PARC). PARC embeds knowledge of underlying physics into its neural network architecture for more robust and accurate prediction of evolving physical fields. PARC was shown to effectively learn complex nonlinear features such as the formation of hotspots and coupled shock fronts in various initiation scenarios of EMs, as a function of microstructures, serving effectively as a microstructure-aware burn model. In this work, we further accelerate PARC and reduce its computational cost by projecting the original dynamics onto a lower-dimensional invariant manifold, or 'latent space.' The projected latent representation encodes the complex geometry of evolving fields (e.g. temperature and pressure) in a set of data-driven features. The reduced dimension of this latent space allows us to learn the dynamics during the initiation of EM with a lighter and more efficient model. We observe a significant decrease in training and inference time while maintaining results comparable to PARC at inference. This work takes steps towards enabling rapid prediction of EM thermomechanics at larger scales and characterization of EM structure-property-performance linkages at a full application scale.

cond-mat.mtrl-sci↗

arXiv2025

Model Order Reduction for Quantum Molecular Dynamics

Molecular dynamics simulations are indispensable for exploring the behavior of atoms and molecules. Grounded in quantum mechanical principles, quantum molecular dynamics provides high predictive power but its computational cost is dominated by iterative high-fidelity electronic structure calculations. We propose a novel model order reduction approach as an alternative to high-fidelity electronic structure calculation. By learning a low-dimensional representation of the electronic solution manifold within the Kohn-Sham density functional theory framework, our model order reduction approach determines the ground state electronic density by projecting the problem onto a low-dimensional subspace, thereby avoiding the computationally expensive iterative optimization of electronic wavefunctions in the full space. We demonstrate the capability of our method on a water molecule, showing excellent agreement with high-fidelity simulations for both molecular geometry and dynamic properties, highlighting the generalizability through carefully designed parametrization and systematic sampling.

physics.chem-ph↗

arXiv2025

Rollout-LaSDI: Enhancing the long-term accuracy of Latent Space Dynamics

cs.LG↗

arXiv2025

Machine-precision energy conservative reduced models for Lagrangian hydrodynamics by quadrature methods

We present an energy conservative, quadrature based model reduction framework for the compressible Euler equations of Lagrangian hydrodynamics. Building on a finite element discretization of the governing equations, we develop reduced models using data based reduced basis functions and the empirical quadrature procedure (EQP). We introduce a strongly energy conservative variant of EQP that enforces exact energy conservation in the reduction process. Numerical experiments for four benchmark problems -- Sedov blast, Gresho vortex, triple point and Taylor-Green vortex -- demonstrate that the numerical implementation of our proposed method conserves total energy to near machine precision, while maintaining accuracy comparable to the basic EQP formulation.

math.NA↗

arXiv2025

Generative Latent Space Dynamics of Electron Density

Modeling the time-dependent evolution of electron density is essential for understanding quantum mechanical behaviors of condensed matter and enabling predictive simulations in spectroscopy, photochemistry, and ultrafast science. Yet, while machine learning methods have advanced static density prediction, modeling its spatiotemporal dynamics remains largely unexplored. In this work, we introduce a generative framework that combines a 3D convolutional autoencoder with a latent diffusion model (LDM) to learn electron density trajectories from ab-initio molecular dynamics (AIMD) simulations. Our method encodes electron densities into a compact latent space and predicts their future states by sampling from the learned conditional distribution, enabling stable long-horizon rollouts without drift or collapse. To preserve statistical fidelity, we incorporate a scaled Jensen-Shannon divergence regularization that aligns generated and reference density distributions. On AIMD trajectories of liquid lithium at 800 K, our model accurately captures both the spatial correlations and the log-normal-like statistical structure of the density. The proposed framework has the potential to accelerate the simulation of quantum dynamics and overcome key challenges faced by current spatiotemporal machine learning methods as surrogates of quantum mechanical simulators.

physics.comp-ph↗

arXiv2025

Latent Space Dynamics Identification for Interface Tracking with Application to Shock-Induced Pore Collapse

Capturing sharp, evolving interfaces remains a central challenge in reduced-order modeling, especially when data is limited and the system exhibits localized nonlinearities or discontinuities. We propose LaSDI-IT (Latent Space Dynamics Identification for Interface Tracking), a data-driven framework that combines low-dimensional latent dynamics learning with explicit interface-aware encoding to enable accurate and efficient modeling of physical systems involving moving material boundaries. At the core of LaSDI-IT is a revised auto-encoder architecture that jointly reconstructs the physical field and an indicator function representing material regions or phases, allowing the model to track complex interface evolution without requiring detailed physical models or mesh adaptation. The latent dynamics are learned through linear regression in the encoded space and generalized across parameter regimes using Gaussian process interpolation with greedy sampling. We demonstrate LaSDI-IT on the problem of shock-induced pore collapse in high explosives, a process characterized by sharp temperature gradients and dynamically deforming pore geometries. The method achieves relative prediction errors below 9% across the parameter space, accurately recovers key quantities of interest such as pore area and hot spot formation, and matches the performance of dense training with only half the data. This latent dynamics prediction was 106 times faster than the conventional high-fidelity simulation, proving its utility for multi-query applications. These results highlight LaSDI-IT as a general, data-efficient framework for modeling discontinuity-rich systems in computational physics, with potential applications in multiphase flows, fracture mechanics, and phase change problems.

physics.comp-ph↗

arXiv2025

Thermodynamically Consistent Latent Dynamics Identification for Parametric Systems

We propose an efficient thermodynamics-informed latent space dynamics identification (tLaSDI) framework for the reduced-order modeling of parametric nonlinear dynamical systems. This framework integrates autoencoders for dimensionality reduction with newly developed parametric GENERIC formalism-informed neural networks (pGFINNs), which enable efficient learning of parametric latent dynamics while preserving key thermodynamic principles such as free energy conservation and entropy generation across the parameter space. To further enhance model performance, a physics-informed active learning strategy is incorporated, leveraging a greedy, residual-based error indicator to adaptively sample informative training data, outperforming uniform sampling at equivalent computational cost. Numerical experiments on the Burgers' equation and the 1D/1V Vlasov-Poisson equation demonstrate that the proposed method achieves up to 3,528x speed-up with 1-3% relative errors, and significant reduction in training (50-90%) and inference (57-61%) cost. Moreover, the learned latent space dynamics reveal the underlying thermodynamic behavior of the system, offering valuable insights into the physical-space dynamics.

cs.LG↗

arXiv2025

mLaSDI: Multi-stage latent space dynamics identification

Accurately solving partial differential equations (PDEs) is essential across many scientific disciplines. However, high-fidelity solvers can be computationally prohibitive, motivating the development of reduced-order models (ROMs). Recently, Latent Space Dynamics Identification (LaSDI) was proposed as a data-driven, non-intrusive ROM framework. LaSDI compresses the training data via an autoencoder and learns user-specified ordinary differential equations (ODEs), governing the latent dynamics, enabling rapid predictions for unseen parameters. While LaSDI has produced effective ROMs for numerous problems, the autoencoder must simultaneously reconstruct the training data and satisfy the imposed latent dynamics, which are often competing objectives that limit accuracy, particularly for complex or high-frequency phenomena. To address this limitation, we propose multi-stage Latent Space Dynamics Identification (mLaSDI). With mLaSDI, we train LaSDI sequentially in stages. After training the initial autoencoder, we train additional decoders which map the latent trajectories to residuals from previous stages. This staged residual learning, combined with periodic activation functions, enables recovery of high-frequency content without sacrificing interpretability of the latent dynamics. We further provide an error decomposition separating autoencoder and latent dynamics contributions, and prove that additional training stages cannot increase the training residual. Numerical experiments on a multiscale oscillating system, unsteady wake flow, and the 1D-1V Vlasov equation demonstrate that mLaSDI achieves significantly lower reconstruction and prediction errors, often by an order of magnitude, while requiring less training time and reduced hyperparameter tuning compared to standard LaSDI.

cs.LG↗