arXiv subjects

Francis J. Alexander

Publications and source records attributed to Francis J. Alexander.

At least 19 recordsLinked to original sources

arXiv2025

Solving Functional PDEs with Gaussian Processes and Applications to Functional Renormalization Group Equations

We present an operator learning framework for solving non-perturbative functional renormalization group equations, which are integro-differential equations defined on functionals. Our proposed approach uses Gaussian process operator learning to construct a flexible functional representation formulated directly on function space, making it independent of a particular equation or discretization. Our method is flexible, and can apply to a broad range of functional differential equations while still allowing for the incorporation of physical priors in either the prior mean or the kernel design. We demonstrate the performance of our method on several relevant equations, such as the Wetterich and Wilson--Polchinski equations, showing that it achieves equal or better performance than existing approximations such as the local-potential approximation, while being significantly more flexible. In particular, our method can handle non-constant fields, making it promising for the study of more complex field configurations, such as instantons.

cs.LG↗

arXiv2025

Reinforcement Learning Closures for Underresolved Partial Differential Equations using Synthetic Data

Partial Differential Equations (PDEs) describe phenomena ranging from turbulence and epidemics to quantum mechanics and financial markets. Despite recent advances in computational science, solving such PDEs for real-world applications remains prohibitively expensive because of the necessity of resolving a broad range of spatiotemporal scales. In turn, practitioners often rely on coarse-grained approximations of the original PDEs, trading off accuracy for reduced computational resources. To mitigate the loss of detail inherent in such approximations, closure models are employed to represent unresolved spatiotemporal interactions. We present a framework for developing closure models for PDEs using synthetic data acquired through the method of manufactured solutions. These data are used in conjunction with reinforcement learning to provide closures for coarse-grained PDEs. We illustrate the efficacy of our method using the one-dimensional and two-dimensional Burgers' equations and the two-dimensional advection equation. Moreover, we demonstrate that closure models trained for inhomogeneous PDEs can be effectively generalized to homogeneous PDEs. The results demonstrate the potential for developing accurate and computationally efficient closure models for systems with scarce data.

cs.LG↗

arXiv2025

HiPerRAG: High-Performance Retrieval Augmented Generation for Scientific Insights

The volume of scientific literature is growing exponentially, leading to underutilized discoveries, duplicated efforts, and limited cross-disciplinary collaboration. Retrieval Augmented Generation (RAG) offers a way to assist scientists by improving the factuality of Large Language Models (LLMs) in processing this influx of information. However, scaling RAG to handle millions of articles introduces significant challenges, including the high computational costs associated with parsing documents and embedding scientific knowledge, as well as the algorithmic complexity of aligning these representations with the nuanced semantics of scientific content. To address these issues, we introduce HiPerRAG, a RAG workflow powered by high performance computing (HPC) to index and retrieve knowledge from more than 3.6 million scientific articles. At its core are Oreo, a high-throughput model for multimodal document parsing, and ColTrast, a query-aware encoder fine-tuning algorithm that enhances retrieval accuracy by using contrastive learning and late-interaction techniques. HiPerRAG delivers robust performance on existing scientific question answering benchmarks and two new benchmarks introduced in this work, achieving 90% accuracy on SciQ and 76% on PubMedQA-outperforming both domain-specific models like PubMedGPT and commercial LLMs such as GPT-4. Scaling to thousands of GPUs on the Polaris, Sunspot, and Frontier supercomputers, HiPerRAG delivers million document-scale RAG workflows for unifying scientific knowledge and fostering interdisciplinary innovation.

cs.IR↗

arXiv2024

Multi-Objective Latent Space Optimization of Generative Molecular Design Models

Molecular design based on generative models, such as variational autoencoders (VAEs), has become increasingly popular in recent years due to its efficiency for exploring high-dimensional molecular space to identify molecules with desired properties. While the efficacy of the initial model strongly depends on the training data, the sampling efficiency of the model for suggesting novel molecules with enhanced properties can be further enhanced via latent space optimization. In this paper, we propose a multi-objective latent space optimization (LSO) method that can significantly enhance the performance of generative molecular design (GMD). The proposed method adopts an iterative weighted retraining approach, where the respective weights of the molecules in the training data are determined by their Pareto efficiency. We demonstrate that our multi-objective GMD LSO method can significantly improve the performance of GMD for jointly optimizing multiple molecular properties.

cs.LG↗

arXiv2023

A Rigorous Uncertainty-Aware Quantification Framework Is Essential for Reproducible and Replicable Machine Learning Workflows

The ability to replicate predictions by machine learning (ML) or artificial intelligence (AI) models and results in scientific workflows that incorporate such ML/AI predictions is driven by numerous factors. An uncertainty-aware metric that can quantitatively assess the reproducibility of quantities of interest (QoI) would contribute to the trustworthiness of results obtained from scientific workflows involving ML/AI models. In this article, we discuss how uncertainty quantification (UQ) in a Bayesian paradigm can provide a general and rigorous framework for quantifying reproducibility for complex scientific workflows. Such as framework has the potential to fill a critical gap that currently exists in ML/AI for scientific workflows, as it will enable researchers to determine the impact of ML/AI model prediction variability on the predictive outcomes of ML/AI-powered workflows. We expect that the envisioned framework will contribute to the design of more reproducible and trustworthy workflows for diverse scientific applications, and ultimately, accelerate scientific discoveries.

cs.LG↗

arXiv2023

Comprehensive analysis of gene expression profiles to radiation exposure reveals molecular signatures of low-dose radiation response

There are various sources of ionizing radiation exposure, where medical exposure for radiation therapy or diagnosis is the most common human-made source. Understanding how gene expression is modulated after ionizing radiation exposure and investigating the presence of any dose-dependent gene expression patterns have broad implications for health risks from radiotherapy, medical radiation diagnostic procedures, as well as other environmental exposure. In this paper, we perform a comprehensive pathway-based analysis of gene expression profiles in response to low-dose radiation exposure, in order to examine the potential mechanism of gene regulation underlying such responses. To accomplish this goal, we employ a statistical framework to determine whether a specific group of genes belonging to a known pathway display coordinated expression patterns that are modulated in a manner consistent with the radiation level. Findings in our study suggest that there exist complex yet consistent signatures that reflect the molecular response to radiation exposure, which differ between low-dose and high-dose radiation.

q-bio.GN↗

arXiv2022

Optimal Decision Making in High-Throughput Virtual Screening Pipelines

The need for efficient computational screening of molecular candidates that possess desired properties frequently arises in various scientific and engineering problems, including drug discovery and materials design. However, the large size of the search space containing the candidates and the substantial computational cost of high-fidelity property prediction models makes screening practically challenging. In this work, we propose a general framework for constructing and optimizing a virtual screening (HTVS) pipeline that consists of multi-fidelity models. The central idea is to optimally allocate the computational resources to models with varying costs and accuracy to optimize the return-on-computational-investment (ROCI). Based on both simulated as well as real data, we demonstrate that the proposed optimal HTVS framework can significantly accelerate screening virtually without any degradation in terms of accuracy. Furthermore, it enables an adaptive operational strategy for HTVS, where one can trade accuracy for efficiency.

math.OC↗

arXiv2021

Adaptive Group Testing with Mismatched Models

Accurate detection of infected individuals is one of the critical steps in stopping any pandemic. When the underlying infection rate of the disease is low, testing people in groups, instead of testing each individual in the population, can be more efficient. In this work, we consider noisy adaptive group testing design with specific test sensitivity and specificity that select the optimal group given previous test results based on pre-selected utility function. As in prior studies on group testing, we model this problem as a sequential Bayesian Optimal Experimental Design (BOED) to adaptively design the groups for each test. We analyze the required number of group tests when using the updated posterior on the infection status and the corresponding Mutual Information (MI) as our utility function for selecting new groups. More importantly, we study how the potential bias on the ground-truth noise of group tests may affect the group testing sample complexity.

stat.ME↗

arXiv2021

Robust Importance Sampling for Error Estimation in the Context of Optimal Bayesian Transfer Learning

Classification has been a major task for building intelligent systems as it enables decision-making under uncertainty. Classifier design aims at building models from training data for representing feature-label distributions--either explicitly or implicitly. In many scientific or clinical settings, training data are typically limited, which makes designing accurate classifiers and evaluating their classification error extremely challenging. While transfer learning (TL) can alleviate this issue by incorporating data from relevant source domains to improve learning in a different target domain, it has received little attention for performance assessment, notably in error estimation. In this paper, we fill this gap by investigating knowledge transferability in the context of classification error estimation within a Bayesian paradigm. We introduce a novel class of Bayesian minimum mean-square error (MMSE) estimators for optimal Bayesian transfer learning (OBTL), which enables rigorous evaluation of classification error under uncertainty in a small-sample setting. Using Monte Carlo importance sampling, we employ the proposed estimator to evaluate the classification accuracy of a broad family of classifiers that span diverse learning capabilities. Experimental results based on both synthetic data as well as real-world RNA sequencing (RNA-seq) data show that our proposed OBTL error estimation scheme clearly outperforms standard error estimators, especially in a small-sample setting, by tapping into the data from other relevant domains.

stat.ML↗

arXiv2020

Resource-Constrained Optimal Experimental Design

The goal of this paper is to make Optimal Experimental Design (OED) computationally feasible for problems involving significant computational expense. We focus exclusively on the Mean Objective Cost of Uncertainty (MOCU), which is a specific methodology for OED, and we propose extensions to MOCU that leverage surrogates and adaptive sampling. We focus on reducing the computational expense associated with evaluating a large set of control policies across a large set of uncertain variables. We propose reducing the computational expense of MOCU by approximating intermediate calculations associated with each parameter/control pair with a surrogate. This surrogate is constructed from sparse sampling and (possibly) refined adaptively through a combination of sensitivity estimation and probabilistic knowledge gained directly from the experimental measurements prescribed from MOCU. We demonstrate our methods on example problems and compare performance relative to surrogate-approximated MOCU with no adaptive sampling and to full MOCU. We find evidence that adaptive sampling does improve performance, but the decision on whether to use surrogate-approximated MOCU versus full MOCU will depend on the relative expense of computation versus experimentation. If computation is more expensive than experimentation, then one should consider using our approach.

math.OC↗

arXiv2007

Equation-free implementation of statistical moment closures

We present a general numerical scheme for the practical implementation of statistical moment closures suitable for modeling complex, large-scale, nonlinear systems. Building on recently developed equation-free methods, this approach numerically integrates the closure dynamics, the equations of which may not even be available in closed form. Although closure dynamics introduce statistical assumptions of unknown validity, they can have significant computational advantages as they typically have fewer degrees of freedom and may be much less stiff than the original detailed model. The closure method can in principle be applied to a wide class of nonlinear problems, including strongly-coupled systems (either deterministic or stochastic) for which there may be no scale separation. We demonstrate the equation-free approach for implementing entropy-based Eyink-Levermore closures on a nonlinear stochastic partial differential equation.

cond-mat.stat-mech↗

arXiv2006

Statistical Mechanics of Histories: A Cluster Monte Carlo Algorithm

We present an efficient computational approach to sample the histories of nonlinear stochastic processes. This framework builds upon recent work on casting a $d$-dimensional stochastic dynamical system into a $d+1$-dimensional equilibrium system using the path integral approach. We introduce a cluster algorithm that efficiently samples histories and discuss how to include measurements that are available into the estimate of the histories. This allows our approach to be applicable to the simulation of rare events and to optimal state and parameter estimation. We demonstrate the utility of this approach for $ϕ^4$ Langevin dynamics in two spatial dimensions where our algorithm improves sampling efficiency up to an order of magnitude.

cond-mat.stat-mech↗

arXiv2000

Fourier Acceleration of Langevin Molecular Dynamics

Fourier acceleration has been successfully applied to the simulation of lattice field theories for more than a decade. In this paper, we extend the method to the dynamics of discrete particles moving in continuum. Although our method is based on a mapping of the particles' dynamics to a regular grid so that discrete Fourier transforms may be taken, it should be emphasized that the introduction of the grid is a purely algorithmic device and that no smoothing, coarse-graining or mean-field approximations are made. The method thus can be applied to the equations of motion of molecular dynamics (MD), or its Langevin or Brownian variants. For example, in Langevin MD simulations our acceleration technique permits a straightforward spectral decomposition of forces so that the long-wavelength modes are integrated with a longer time step, thereby reducing the time required to reach equilibrium or to decorrelate the system in equilibrium. Speedup factors of up to 30 are observed relative to pure (unaccelerated) Langevin MD. As with acceleration of critical lattice models, even further gains relative to the unaccelerated method are expected for larger systems. Preliminary results for Fourier-accelerated molecular dynamics are presented in order to illustrate the basic concepts. Possible extensions of the method and further lines of research are discussed.

cond-mat.stat-mech↗

arXiv1999

Coulomb field of an accelerated charge: physical and mathematical aspects

The Maxwell field equations relative to a uniformly accelerated frame, and the variational principle from which they are obtained, are formulated in terms of the technique of geometrical gauge invariant potentials. They refer to the transverse magnetic (TM) and the transeverse electric (TE) modes. This gauge invariant "2+2" decomposition is used to see how the Coulomb field of a charge, static in an accelerated frame, has properties that suggest features of electromagnetism which are different from those in an inertial frame. In particular, (1) an illustrative calculation shows that the Larmor radiation reaction equals the electrostatic attraction between the accelerated charge and the charge induced on the surface whose history is the event horizon, and (2) a spectral decomposition of the Coulomb potential in the accelerated frame suggests the possibility that the distortive effects of this charge on the Rindler vacuum are akin to those of a charge on a crystal lattice.

gr-qc↗

arXiv1998

Shape-Dependent Thermodynamics and Non-Local Hydrodynamics in a Non-Gibbsian Steady-State of a Drift-Diffusion System

Shape-dependent thermodynamics and non-local hydrodynamics are argued to occur in dissipative steady states of driven diffusive systems. These predictions are confirmed by numerical simulations. Unlike power-law correlations, these phenomena cannot be explained by a hypothesis of ``criticality''. Instead, they require the effective Hamiltonian of the system to contain very long-range potentials, making the invariant probability measures formally ``non-Gibbsian''.

cond-mat.stat-mech↗

arXiv1996

Turbulence Fluctuations and New Universal Realizability Conditions in Modelling

General turbulent mean statistics are shown to be characterized by a variational principle. The variational functionals, or ``effective actions'', have experimental consequences for turbulence fluctuations and are subject to realizability conditions of positivity and convexity. An efficient Rayleigh-Ritz algorithm is available to calculate approximate effective actions within PDF closures. Examples are given for Navier-Stokes and for a 3-mode system of Lorenz. The new realizability conditions succeed at detecting {\em a priori} the poor predictions of PDF closures even when the classical 2nd-order moment realizability conditions are satisfied.

chao-dyn↗

arXiv1996

Rayleigh-Ritz Calculation of Effective Potential Far From Equilibrium

We demonstrate the utility of a Rayleigh-Ritz scheme recently proposed to compute the nonequilibrium effective potential nonperturbatively in a strong noise regime far from equilibrium. A simple Kramers model of an ionic conductor is used to illustrate the efficiency of the method.

chao-dyn↗

arXiv1996

Integer Lattice Gases

We generalize the hydrodynamic lattice gas model to include arbitrary numbers of particles moving in each lattice direction. For this generalization we derive the equilibrium distribution function and the hydrodynamic equations, including the equation of state and the prefactor of the inertial term that arises from the breaking of galilean invariance in these models. We show that this prefactor can be set to unity in the generalized model, therby effectively restoring galilean invariance. Moreover, we derive an expression for the kinematic viscosity, and show that it tends to decrease with the maximum number of particles allowed in each direction, so that higher Reynolds numbers may be achieved. Finally, we derive expressions for the statistical noise and the Boltzmann entropy of these models.

comp-gas↗