arXiv subjects

Julie Pham

Publications and source records attributed to Julie Pham.

3 recordsLinked to original sources

arXiv2026

Real-time inverse solutions via neural matrix operators

Rapid data assimilation is required for real-time prediction and control in digital twins. For many physical systems, the data assimilation task requires the solution of a physics-constrained inverse problem, which is often computationally intractable in real time using traditional physics solvers. This work presents a reduced-basis neural operator approach to enable real-time inverse problem solutions in the digital twin setting. Our approach specifically targets the large class of problems with spatiotemporal dynamics governed by partial differential equations (PDEs) that are parameterized nonlinearly with respect to model parameters $m$, and linearly with respect to inversion parameters $q$. Based on this physical structure, our neural operator approximates the nonlinear map from the model parameters $m$ to the parameter-to-observable operator $\mathcal{F}(m)$ in a reduced subspace. Since the output of the neural operator is the parameter-to-observable operator itself (manifested as a matrix), we refer to this approach as NEural Matrix Operator (NEMO). With NEMO, for new given $m$, we enable a closed-form inverse problem solution for $q$ in a reduced subspace. We apply NEMO in two real-world applications: contaminant transport initial condition identification, and hypersonic vehicle load identification. We show that NEMO delivers high quality inverse problem solutions for data assimilation in real time, with over three orders of magnitude speedup compared to constructing the reduced operator with the PDE solver. Further, NEMO demonstrates comparable inverse performance to a state-of-the-art multiple-input neural operator, while reducing online computational complexity by over an order of magnitude and providing real-time uncertainty quantification.

math.NA↗

arXiv2025

Projection-based multifidelity linear regression for data-scarce applications

Surrogate modeling for systems with high-dimensional quantities of interest remains challenging, particularly when training data are costly to acquire. This work develops multifidelity methods for multiple-input multiple-output linear regression targeting data-limited applications with high-dimensional outputs. Multifidelity methods integrate many inexpensive low-fidelity model evaluations with limited, costly high-fidelity evaluations. We introduce two projection-based multifidelity linear regression approaches with linear and nonlinear features that leverage principal component basis vectors for dimensionality reduction and combine multifidelity data through: (i) a direct data augmentation using low-fidelity data, and (ii) a data augmentation incorporating explicit linear corrections between low-fidelity and high-fidelity data. The data augmentation approaches combine high-fidelity and low-fidelity data into a unified training set and train the linear regression model through weighted least squares with fidelity-specific weights. We introduce a proximity-based weighting scheme with automatic weight selection strategy through cross-validation. The proposed multifidelity linear regression methods are demonstrated on approximating the surface pressure field of a hypersonic vehicle in flight and the temperature field on an aircraft disc braking system. In an ultra low-data regime of no more than twelve high-fidelity samples, multifidelity linear regression achieves approximately 2%-12% improvement in median accuracy and a higher $R^2$ score relative to single-fidelity methods at comparable computational cost.

stat.ML↗

arXiv2024

Real-time aerodynamic load estimation for hypersonics via strain-based inverse maps

This work develops an efficient real-time inverse formulation for inferring the aerodynamic surface pressures on a hypersonic vehicle from sparse measurements of the structural strain. The approach aims to provide real-time estimates of the aerodynamic loads acting on the vehicle for ground and flight testing, as well as guidance, navigation, and control applications. Specifically, the approach targets hypersonic flight conditions where direct measurement of the surface pressures is challenging due to the harsh aerothermal environment. For problems employing a linear elastic structural model, we show that the inference problem can be posed as a least-squares problem with a linear constraint arising from a finite element discretization of the governing elasticity partial differential equation. Due to the linearity of the problem, an explicit solution is given by the normal equations. Pre-computation of the resulting inverse map enables rapid evaluation of the surface pressure and corresponding integrated quantities, such as the force and moment coefficients. The inverse approach additionally allows for uncertainty quantification, providing insights for theoretical recoverability and robustness to sensor noise. Numerical studies demonstrate the estimator performance for reconstructing the surface pressure field, as well as the force and moment coefficients, for the Initial Concept 3.X (IC3X) conceptual hypersonic vehicle.

math.NA↗