arXiv subjects

Nathan M. Urban

Publications and source records attributed to Nathan M. Urban.

At least 19 recordsLinked to original sources

arXiv2026

Machine learning assisted Bayesian calibration of an accelerator digital twin from orbit response data

Digital twins of particle accelerators are used to plan and control operations and to design data collection campaigns. Accurate modeling typically requires knowledge of quantities that are hard to measure directly, e.g., magnet alignments, transfer functions relating power supply currents to magnetic fields, magnet nonlinearities, and stray fields. In this work we introduce multiplicative parameters to the quadrupole transfer functions to parametrize these effects. We use Bayesian methods to probabilistically estimate these parameters and their uncertainties by calibrating the Bmad digital twin to beam measurements performed at the AGS Booster at Brookhaven National Laboratory. The inference is computationally accelerated using a machine learning emulator of the physical accelerator digital twin trained to a perturbed-parameter ensemble of Bmad simulations. The result is a joint posterior distribution over the parameters constrained by the data, taking into account beam monitor errors. Incorporating estimates of the parameters into the digital twin is shown to result in a significant improvement in the quality of the model and provides error bars on the model parameters and predictions.

physics.acc-ph↗

arXiv2026

Flexible and Stable Dynamics Discovery with Onsager's Variational Principle

Variational principles specify the dynamics of a physical system via the extremization of associated functional data. Onsager's variational principle (OVP), which characterizes dissipation-dominated phenomena such as phase separation, admits an unconditionally energy-stable time discretization through the minimization of a Rayleighan functional combining free energy and dissipative effects. The present work considers the case where one or more parts of this functional are empirically approximated or otherwise uncertain. To address this, a novel variational discretization of OVP is introduced which recovers previous work as a special case, and a learning problem is formulated which identifies uncertain terms in the free energy and dissipation potential from observable data. It is shown that the resulting OVP-based models connect directly to previous work in terms of proximal methods, Sobolev and Wasserstein gradient flows, while remaining provably energy-stable under arbitrarily long rollouts. The approach is illustrated on examples including Allen-Cahn, Fokker-Planck, and Cahn-Hilliard system models, where the effects of bulk free-energy densities, nonlocal potentials, and nonstandard boundary conditions are effectively learned with model classes consisting of polynomials, shallow neural networks, and spectral convolution kernels.

math.DS↗

arXiv2026

Data-efficient surrogate modeling of spectral functions using Gaussian processes: An application to the $t$-$t'$-$t''$-$J$ model

Spectral functions encode key many-body information but are costly to compute with high fidelity. Machine-learning surrogates have emerged as a powerful alternative, yet many approaches require large training datasets. We develop a data-efficient surrogate for spectral functions using the $t$-$t'$-$t''$-$J$ model, which describes the motion of a hole in a quantum antiferromagnet. Using $\sim$ 10$^5$ self-consistent Born approximation-based spectra from Lee, Carbone and Yin (Phys. Rev. B 107, 205132 (2023)), we train a deep-kernel Gaussian process surrogate model with sparse variational inference (DKL-SVGP) using only 10% of the available training spectra. We benchmark against feed-forward neural networks (FFNN) trained on the same reduced subset and on the full dataset. The proposed DKL-SVGP model consistently outperforms the reduced-data FFNN and, despite using only 10% of the training spectra, achieves spectrum-wise errors within the same order-of-magnitude as the full-data FFNN baseline. Worst-tail diagnostics show improved fidelity on difficult spectra, while peak-level analysis indicates that DKL-SVGP recovers dominant peak heights with comparable accuracy and improves peak-location agreement under a matched-peak evaluation that mitigates rare peak-swapping cases. Overall, these results highlight GP-based surrogates as a competitive and data-efficient approach for spectral-function prediction in scarce-data regimes.

cond-mat.str-el↗

arXiv2025

C-LoRA: Contextual Low-Rank Adaptation for Uncertainty Estimation in Large Language Models

Low-Rank Adaptation (LoRA) offers a cost-effective solution for fine-tuning large language models (LLMs), but it often produces overconfident predictions in data-scarce few-shot settings. To address this issue, several classical statistical learning approaches have been repurposed for scalable uncertainty-aware LoRA fine-tuning. However, these approaches neglect how input characteristics affect the predictive uncertainty estimates. To address this limitation, we propose Contextual Low-Rank Adaptation (C-LoRA) as a novel uncertainty-aware and parameter efficient fine-tuning approach, by developing new lightweight LoRA modules contextualized to each input data sample to dynamically adapt uncertainty estimates. Incorporating data-driven contexts into the parameter posteriors, C-LoRA mitigates overfitting, achieves well-calibrated uncertainties, and yields robust predictions. Extensive experiments on LLaMA2-7B models demonstrate that C-LoRA consistently outperforms the state-of-the-art uncertainty-aware LoRA methods in both uncertainty quantification and model generalization. Ablation studies further confirm the critical role of our contextual modules in capturing sample-specific uncertainties. C-LoRA sets a new standard for robust, uncertainty-aware LLM fine-tuning in few-shot regimes. Although our experiments are limited to 7B models, our method is architecture-agnostic and, in principle, applies beyond this scale; studying its scaling to larger models remains an open problem. Our code is available at https://github.com/ahra99/c_lora.

cs.LG↗

arXiv2025

Data-Augmented Few-Shot Neural Emulator for Computer-Model System Identification

Partial differential equations (PDEs) underpin the modeling of many natural and engineered systems. It can be convenient to express such models as neural PDEs rather than using traditional numerical PDE solvers by replacing part or all of the PDE's governing equations with a neural network representation. Neural PDEs are often easier to differentiate, linearize, reduce, or use for uncertainty quantification than the original numerical solver. They are usually trained on solution trajectories obtained by long-horizon rollout of the PDE solver. Here we propose a more sample-efficient data-augmentation strategy for generating neural PDE training data from a computer model by space-filling sampling of local "stencil" states. This approach removes a large degree of spatiotemporal redundancy present in trajectory data and oversamples states that may be rarely visited but help the neural PDE generalize across the state space. We demonstrate that accurate neural PDE stencil operators can be learned from synthetic training data generated by the computational equivalent of 10 timesteps' worth of numerical simulation. Accuracy is further improved if we assume access to a single full-trajectory simulation from the computer model, which is typically available in practice. Across several PDE systems, we show that our data-augmented stencil data yield better trained neural stencil operators, with clear performance gains compared with naively sampled stencil data from simulation trajectories. Finally, with only 10 solver steps' worth of augmented stencil data, our approach outperforms traditional ML emulators trained on thousands of trajectories in long-horizon rollout accuracy and stability.

cs.LG↗

arXiv2025

Robust, Online, and Adaptive Decentralized Gaussian Processes

Gaussian processes (GPs) offer a flexible, uncertainty-aware framework for modeling complex signals, but scale cubically with data, assume static targets, and are brittle to outliers, limiting their applicability in large-scale problems with dynamic and noisy environments. Recent work introduced decentralized random Fourier feature Gaussian processes (DRFGP), an online and distributed algorithm that casts GPs in an information-filter form, enabling exact sequential inference and fully distributed computation without reliance on a fusion center. In this paper, we extend DRFGP along two key directions: first, by introducing a robust-filtering update that downweights the impact of atypical observations; and second, by incorporating a dynamic adaptation mechanism that adapts to time-varying functions. The resulting algorithm retains the recursive information-filter structure while enhancing stability and accuracy. We demonstrate its effectiveness on a large-scale Earth system application, underscoring its potential for in-situ modeling.

stat.ML↗

arXiv2025

Uncertainty-Aware Adaptation of Large Language Models for Protein-Protein Interaction Analysis

Identification of protein-protein interactions (PPIs) helps derive cellular mechanistic understanding, particularly in the context of complex conditions such as neurodegenerative disorders, metabolic syndromes, and cancer. Large Language Models (LLMs) have demonstrated remarkable potential in predicting protein structures and interactions via automated mining of vast biomedical literature; yet their inherent uncertainty remains a key challenge for deriving reproducible findings, critical for biomedical applications. In this study, we present an uncertainty-aware adaptation of LLMs for PPI analysis, leveraging fine-tuned LLaMA-3 and BioMedGPT models. To enhance prediction reliability, we integrate LoRA ensembles and Bayesian LoRA models for uncertainty quantification (UQ), ensuring confidence-calibrated insights into protein behavior. Our approach achieves competitive performance in PPI identification across diverse disease contexts while addressing model uncertainty, thereby enhancing trustworthiness and reproducibility in computational biology. These findings underscore the potential of uncertainty-aware LLM adaptation for advancing precision medicine and biomedical research.

cs.LG↗

arXiv2025

Cost-effective Reduced-Order Modeling via Bayesian Active Learning

Machine Learning surrogates have been developed to accelerate solving systems dynamics of complex processes in different science and engineering applications. To faithfully capture governing systems dynamics, these methods rely on large training datasets, hence restricting their applicability in real-world problems. In this work, we propose BayPOD-AL, an active learning framework based on an uncertainty-aware Bayesian proper orthogonal decomposition (POD) approach, which aims to effectively learn reduced-order models from high-fidelity full-order models representing complex systems. Experimental results on predicting the temperature evolution over a rod demonstrate BayPOD-AL's effectiveness in suggesting the informative data and reducing computational cost related to constructing a training dataset compared to other uncertainty-guided active learning strategies. Furthermore, we demonstrate BayPOD-AL's generalizability and efficiency by evaluating its performance on a dataset of higher temporal resolution than the training dataset.

cs.LG↗

arXiv2024

Pathway-Guided Optimization of Deep Generative Molecular Design Models for Cancer Therapy

The data-driven drug design problem can be formulated as an optimization task of a potentially expensive black-box objective function over a huge high-dimensional and structured molecular space. The junction tree variational autoencoder (JTVAE) has been shown to be an efficient generative model that can be used for suggesting legitimate novel drug-like small molecules with improved properties. While the performance of the generative molecular design (GMD) scheme strongly depends on the initial training data, one can improve its sampling efficiency for suggesting better molecules with enhanced properties by optimizing the latent space. In this work, we propose how mechanistic models - such as pathway models described by differential equations - can be used for effective latent space optimization(LSO) of JTVAEs and other similar models for GMD. To demonstrate the potential of our proposed approach, we show how a pharmacodynamic model, assessing the therapeutic efficacy of a drug-like small molecule by predicting how it modulates a cancer pathway, can be incorporated for effective LSO of data-driven models for GMD.

cs.LG↗

arXiv2024

Implicit Neural Representations for Simultaneous Reduction and Continuous Reconstruction of Multi-Altitude Climate Data

The world is moving towards clean and renewable energy sources, such as wind energy, in an attempt to reduce greenhouse gas emissions that contribute to global warming. To enhance the analysis and storage of wind data, we introduce a deep learning framework designed to simultaneously enable effective dimensionality reduction and continuous representation of multi-altitude wind data from discrete observations. The framework consists of three key components: dimensionality reduction, cross-modal prediction, and super-resolution. We aim to: (1) improve data resolution across diverse climatic conditions to recover high-resolution details; (2) reduce data dimensionality for more efficient storage of large climate datasets; and (3) enable cross-prediction between wind data measured at different heights. Comprehensive testing confirms that our approach surpasses existing methods in both super-resolution quality and compression efficiency.

cs.LG↗

arXiv2024

Understanding Uncertainty-based Active Learning Under Model Mismatch

Instead of randomly acquiring training data points, Uncertainty-based Active Learning (UAL) operates by querying the label(s) of pivotal samples from an unlabeled pool selected based on the prediction uncertainty, thereby aiming at minimizing the labeling cost for model training. The efficacy of UAL critically depends on the model capacity as well as the adopted uncertainty-based acquisition function. Within the context of this study, our analytical focus is directed toward comprehending how the capacity of the machine learning model may affect UAL efficacy. Through theoretical analysis, comprehensive simulations, and empirical studies, we conclusively demonstrate that UAL can lead to worse performance in comparison with random sampling when the machine learning model class has low capacity and is unable to cover the underlying ground truth. In such situations, adopting acquisition functions that directly target estimating the prediction performance may be beneficial for improving the performance of UAL.

cs.LG↗

arXiv2024

Sequential Bayesian Neural Subnetwork Ensembles

Deep ensembles have emerged as a powerful technique for improving predictive performance and enhancing model robustness across various applications by leveraging model diversity. However, traditional deep ensemble methods are often computationally expensive and rely on deterministic models, which may limit their flexibility. Additionally, while sparse subnetworks of dense models have shown promise in matching the performance of their dense counterparts and even enhancing robustness, existing methods for inducing sparsity typically incur training costs comparable to those of training a single dense model, as they either gradually prune the network during training or apply thresholding post-training. In light of these challenges, we propose an approach for sequential ensembling of dynamic Bayesian neural subnetworks that consistently maintains reduced model complexity throughout the training process while generating diverse ensembles in a single forward pass. Our approach involves an initial exploration phase to identify high-performing regions within the parameter space, followed by multiple exploitation phases that take advantage of the compactness of the sparse model. These exploitation phases quickly converge to different minima in the energy landscape, corresponding to high-performing subnetworks that together form a diverse and robust ensemble. We empirically demonstrate that our proposed approach outperforms traditional dense and sparse deterministic and Bayesian ensemble models in terms of prediction accuracy, uncertainty estimation, out-of-distribution detection, and adversarial robustness.

stat.ML↗

arXiv2024

Multi-modal Representation Learning for Cross-modal Prediction of Continuous Weather Patterns from Discrete Low-Dimensional Data

World is looking for clean and renewable energy sources that do not pollute the environment, in an attempt to reduce greenhouse gas emissions that contribute to global warming. Wind energy has significant potential to not only reduce greenhouse emission, but also meet the ever increasing demand for energy. To enable the effective utilization of wind energy, addressing the following three challenges in wind data analysis is crucial. Firstly, improving data resolution in various climate conditions to ensure an ample supply of information for assessing potential energy resources. Secondly, implementing dimensionality reduction techniques for data collected from sensors/simulations to efficiently manage and store large datasets. Thirdly, extrapolating wind data from one spatial specification to another, particularly in cases where data acquisition may be impractical or costly. We propose a deep learning based approach to achieve multi-modal continuous resolution wind data prediction from discontinuous wind data, along with data dimensionality reduction.

cs.LG↗

arXiv2023

Identifying Bayesian Optimal Experiments for Uncertain Biochemical Pathway Models

Pharmacodynamic (PD) models are mathematical models of cellular reaction networks that include drug mechanisms of action. These models are useful for studying predictive therapeutic outcomes of novel drug therapies in silico. However, PD models are known to possess significant uncertainty with respect to constituent parameter data, leading to uncertainty in the model predictions. Furthermore, experimental data to calibrate these models is often limited or unavailable for novel pathways. In this study, we present a Bayesian optimal experimental design approach for improving PD model prediction accuracy. We then apply our method using simulated experimental data to account for uncertainty in hypothetical laboratory measurements. This leads to a probabilistic prediction of drug performance and a quantitative measure of which prospective laboratory experiment will optimally reduce prediction uncertainty in the PD model. The methods proposed here provide a way forward for uncertainty quantification and guided experimental design for models of novel biological pathways.

q-bio.MN↗

arXiv2023

Learning Active Subspaces for Effective and Scalable Uncertainty Quantification in Deep Neural Networks

Bayesian inference for neural networks, or Bayesian deep learning, has the potential to provide well-calibrated predictions with quantified uncertainty and robustness. However, the main hurdle for Bayesian deep learning is its computational complexity due to the high dimensionality of the parameter space. In this work, we propose a novel scheme that addresses this limitation by constructing a low-dimensional subspace of the neural network parameters-referred to as an active subspace-by identifying the parameter directions that have the most significant influence on the output of the neural network. We demonstrate that the significantly reduced active subspace enables effective and scalable Bayesian inference via either Monte Carlo (MC) sampling methods, otherwise computationally intractable, or variational inference. Empirically, our approach provides reliable predictions with robust uncertainty estimates for various regression tasks.

stat.ML↗

arXiv2020

A Bayesian approach to regional decadal predictability: Sparse parameter estimation in high-dimensional linear inverse models of high-latitude sea surface temperature variability

Stochastic reduced models are an important tool in climate systems whose many spatial and temporal scales cannot be fully discretized or underlying physics may not be fully accounted for. One form of reduced model, the linear inverse model (LIM), has been widely used for regional climate predictability studies - typically focusing more on tropical or mid-latitude studies. However, most LIM fitting techniques rely on point estimation techniques deriving from fluctuation-dissipation theory. In this methodological study we explore the use of Bayesian inference techniques for LIM parameter estimation of sea surface temperature (SST), to quantify the skillful decadal predictability of Bayesian LIM models at high latitudes. We show that Bayesian methods, when compared to traditional point estimation methods for LIM-type models, provide better calibrated probabilistic skill, while simultaneously providing better point estimates due to the regularization effect of the prior distribution in high-dimensional problems. We compare the effect of several priors, as well as maximum likelihood estimates, on (1) estimating parameter values on a perfect model experiment and (2) producing calibrated 1-year SST anomaly forecast distributions using a pre-industrial control run of the Community Earth System Model (CESM). Finally, we employ a host of probabilistic skill metrics to determine the extent to which a LIM can forecast SST anomalies at high latitudes. We find that the choice of prior distribution has an appreciable impact on estimation outcomes, and priors that emphasize physically relevant properties enhance the model's ability to capture variability of SST anomalies.

stat.ME↗

arXiv2019

Scalable Extended Dynamic Mode Decomposition using Random Kernel Approximation

The Koopman operator is a linear, infinite-dimensional operator that governs the dynamics of system observables; Extended Dynamic Mode Decomposition (EDMD) is a data-driven method for approximating the Koopman operator using functions (features) of the system state snapshots. This paper investigates an approach to EDMD in which the features used provide random approximations to a particular kernel function. The objective of this is computational economy for large data sets: EDMD is generally ill-suited for problems with large state dimension, and its dual kernel formulation (KDMD) is well-suited for such problems only if the number of data snapshots is relatively small. We discuss two specific methods for generating features: random Fourier features, and the Nystrom method. The first method is a data-independent method for translation-invariant kernels only and involves random sampling in feature space; the second method is a data-dependent empirical method that may be used for any kernel and involves random sampling of data. We first discuss how these ideas may be applied in an EDMD context, as well as a means for adaptively adding random Fourier features. We demonstrate these methods on two example problems and conclude with an analysis of the relative benefits and drawbacks of each method.

math.NA↗

arXiv2019

Improved Representation of Ocean Heat Content in Energy Balance Models

Anomaly-diffusing energy balance models (AD-EBM) are routinely employed to analyze and emulate the warming response of both observed and simulated Earth systems. We demonstrate a deficiency in common multi-layer as well as continuous-diffusion AD-EBM variants: They are unable to, simultaneously, properly represent surface warming and the vertical distribution of heat uptake. We show that this inability is due to the diffusion approximation. On the other hand, it is well understood that transport of water from the surface mixed layer into the ocean interior is achieved, in large part, by the process of ventilation---a process associated with outcropping isopycnals. We, therefore, start from a configuration of outcropping isopycnals and demonstrate how an AD-EBM can be modified to include the effect of ventilation on ocean uptake of anomalous radiative forcing. The resulting EBM is able to successfully represent both surface warming and the vertical distribution of heat uptake, and indeed, a simple four layer model suffices. The simplicity of the models notwithstanding, the analysis presented and the necessity of the modification highlight the role played by processes related to the down-welling branch of global ocean circulation in shaping the vertical distribution of ocean heat uptake.

physics.ao-ph↗