arXiv subjects

Joanna Zou

Publications and source records attributed to Joanna Zou.

4 recordsLinked to original sources

arXiv2026

Goal-oriented learning of stochastic differential equations using error bounds on path-space observables

Stochastic differential equations (SDEs), which serve as the governing equations for dynamical systems in a broad range of applications, can become cost-prohibitive for numerical simulation at scales necessary for quantifying key properties. Surrogate models of the drift function of an SDE, learned from data of the high-fidelity system, are routinely used to increase the efficiency of simulation and prediction of properties. However, standard choices of loss function for learning the surrogate model fail to provide error guarantees in certain path-dependent observables, such as transition times. This paper introduces an error bound for path-space observables and employs it as a novel variational loss for the goal-oriented learning of the drift function of a SDE. We show the error bound holds for a broad class of observables, including mean first hitting times on unbounded time domains. We derive an analytical gradient of the goal-oriented loss by leveraging the formula for Fréchet derivatives of expected path functionals, which remains tractable for implementation in stochastic gradient descent schemes. We demonstrate that surrogate models of overdamped Langevin systems developed via goal-oriented learning achieve improved accuracy in predicting the statistics of a first hitting time observable and robustness to distributional shift in the data.

stat.ME↗

arXiv2026

Stein Kernelized Molecular Dynamics for Active Learning of Interatomic Potentials

Machine learning interatomic potentials (MLIPs) enable efficient and accurate atomistic simulations but depend critically on the quality and diversity of the training data. We introduce Stein kernelized molecular dynamics (SKMD), an enhanced sampling method that uses interacting particle dynamics to acquire informative training configurations for the active learning and fine-tuning of MLIPs. SKMD corresponds to a stochastic variant of Stein variational gradient descent that is adapted for molecular dynamics by incorporating asynchronous particle updates and a kernel of global atomic descriptors, which provides a symmetry-aware measure of configurational similarity. Unlike other enhanced samplers used in molecular dynamics, SKMD preserves the Boltzmann distribution as the asymptotic distribution of the dynamics. This property enforces a balance between the exploration of diverse configurations and attraction toward high-probability regions of the energy landscape. We further propose an approach to efficient online data acquisition using an adaptive stopping criterion that selects non-redundant training data over the course of simulation. We demonstrate SKMD for the active learning of a neural network model of the Müller-Brown potential and the fine-tuning of a MACE interatomic potential for alanine dipeptide. Compared to active learning baselines, our method achieves higher model accuracy in fewer training iterations with the same number of acquired training samples.

cs.LG↗

arXiv2026

Data Curation for Machine Learning Interatomic Potentials by Determinantal Point Processes

The development of machine learning interatomic potentials faces a critical computational bottleneck with the generation and labeling of useful training datasets. We present a novel application of determinantal point processes (DPPs) to the task of selecting informative subsets of atomic configurations to label with reference energies and forces from costly quantum mechanical methods. Through experiments with hafnium oxide data, we show that DPPs are competitive with existing approaches to constructing compact but diverse training sets by utilizing kernels of molecular descriptors, leading to improved accuracy and robustness in machine learning representations of molecular systems. Our work identifies promising directions to employ DPPs for unsupervised training data curation with heterogeneous or multimodal data, or in online active learning schemes for iterative data augmentation during molecular dynamics simulation.

stat.AP↗

arXiv2023

Virtual sensing of subsoil strain response in monopile-based offshore wind turbines via Gaussian process latent force models

Virtual sensing techniques have gained traction in applications to the structural health monitoring of monopile-based offshore wind turbines, as the strain response below the mudline, which is a primary indicator of fatigue damage accumulation, is impractical to measure directly with physical instrumentation. The Gaussian process latent force model (GPFLM) is a generalized Bayesian virtual sensing technique which combines a physics-driven model of the structure with a data-driven model of latent variables of the system to extrapolate unmeasured strain states. In the GPLFM, modeling of unknown sources of excitation as a Gaussian process (GP) serves to facilitate strain estimation by providing a complete stochastic characterization of the covariance relationship between input forces and states, using properties of the GP covariance kernel as well as correlation information supplied by the mechanical model. It is shown that posterior inference of the latent inputs and states is performed by Gaussian process regression of measured accelerations, computed efficiently using Kalman filtering and Rauch-Tung-Striebel smoothing in an augmented state-space model. While the GPLFM has been previously demonstrated in numerical studies to improve upon other virtual sensing techniques in terms of accuracy, robustness, and numerical stability, this work provides one of the first cases of in-situ validation of the GPLFM. The predicted strain response by the GPLFM is compared to subsoil strain data collected from an operating offshore wind turbine in the Westermeerwind Park in the Netherlands.

stat.AP↗