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Sampling Decisions

arXiv 2025年

作者： Chertkov, Michael Ahn, Sungsoo Behjoo, Hamidreza Program in Applied Mathematics Department of Mathematics University of Arizona TucsonAZ United States Graduate School of AI KAIST Korea Republic of

In this manuscript, we introduce a novel Decision Flow (DF) framework for sampling decisions from a target distribution while incorporating additional guidance from a prior sampler. DF can be viewed as an AI-driven algorithmic reincarnation of the Markov Decision Process (MDP) approach in Stochastic Optimal Control. It extends the continuous-space, continuous-time Path Integral Diffusion sampling technique of [1] to discrete time and space, while also generalizing the Generative Flow Network framework of [2]. In its most basic form – an explicit, Neural Network (NN)-free formulation – DF leverages the linear solvability of the underlying MDP [3] to adjust the transition probabilities of the prior sampler. The resulting Markov process is expressed as a convolution of the reverse-time Green’s function of the prior sampling with the target distribution. We illustrate the DF framework through an example of sampling from the Ising model, discuss potential NN-based extensions, and outline how DF can enhance guided sampling across various applications. Copyright © 2025, The Authors. All rights reserved.

关键词： Stochastic systems

Machine learning of microstructure–property relationships in materials with robust features from foundational vision transformers

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arXiv 2025年

作者： Whitman, Sheila E. Latypov, Marat I. Graduate Interdisciplinary Program in Applied Mathematics University of Arizona TucsonAZ85721 United States Department of Materials Science and Engineering University of Arizona TucsonAZ85721 United States

Machine learning of microstructure–property relationships from data is an emerging approach in computational materials science. Most existing machine learning efforts focus on the development of task-specific models for each microstructure–property relationship. We propose utilizing pre-trained foundational vision transformers for the extraction of task-agnostic microstructure features and subsequent light-weight machine learning of a microstructure-dependent property. We demonstrate our approach with pre-trained state-of-the-art vision transformers (CLIP, DINOV2, SAM) in two case studies on machine-learning: (i) elastic modulus of two-phase microstructures based on simulations data;and (ii) Vicker’s hardness of Ni-base and Co-base superalloys based on experimental data published in literature. Our results show the potential of foundational vision transformers for robust microstructure representation and efficient machine learning of microstructure–property relationships without the need for expensive task-specific training or fine-tuning of bespoke deep learning models. © 2025, CC BY.

关键词： Elastic moduli

Optional participation only provides a narrow scope for sustaining cooperation

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Physical Review E 2025年第2期111卷 024306-024306页

作者： Khadija Khatun Chen Shen Jun Tanimoto Interdisciplinary Graduate School of Engineering Sciences Kyushu University Fukuoka 816-8580 Japan Department of Applied Mathematics University of Dhaka Dhaka-1000 Bangladesh Faculty of Engineering Sciences Kyushu University Kasuga-koen Kasuga-shi Fukuoka 816-8580 Japan

Understanding how cooperation emerges in public goods games is crucial for addressing societal challenges. While optional participation can establish cooperation without identifying cooperators, it relies on specific assumptions—that individuals abstain and receive a non-negative payoff, or that nonparticipants cause damage to public goods—which limits our understanding of its broader role. We generalize this mechanism by considering nonparticipants' payoffs and their potential direct influence on public goods, allowing us to examine how various strategic motives for nonparticipation affect cooperation. Using replicator dynamics, we find that cooperation thrives only when nonparticipants are motivated by individualistic or prosocial values, with individualistic motivations yielding optimal cooperation. These findings are robust to mutation, which slightly enlarges the region where cooperation can be maintained through cyclic dominance among strategies. Our results suggest that while optional participation can benefit cooperation, its effectiveness is limited and highlights the limitations of bottom-up schemes in supporting public goods.

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A simple yet effective approach for predicting disease spread using mathematically-inspired diffusion-informed neural networks

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Scientific Reports 2025年第1期15卷 1-14页

作者： Jeong, ByeongChang Lee, Yeon Ju Han, Cheol E. Department of Electronics and Information Engineering Korea University Sejong South Korea Interdisciplinary Graduate Program for Artificial Intelligence Smart Convergence Technology Korea University 2511 Sejong-ro Sejong 30019 South Korea Department of Applied Mathematics Korea University Sejong South Korea

The COVID-19 outbreak has highlighted the importance of mathematical epidemic models like the Susceptible-Infected-Recovered (SIR) model, for understanding disease spread dynamics. However, enhancing their predictive accuracy complicates parameter estimation. To address this, we proposed a novel model that integrates traditional mathematical modeling with deep learning which has shown improved predicted power across diverse fields. The proposed model includes a simple artificial neural network (ANN) for regional disease incidences, and a graph convolutional neural network (GCN) to capture spread to adjacent regions. GCNs are a recent deep learning algorithm designed to learn spatial relationship from graph-structured data. We applied the model to COVID-19 incidences in Spain to evaluate its performance. It achieved a 0.9679 correlation with the test data, outperforming previous models with fewer parameters. By leveraging the efficient training methods of deep learning, the model simplifies parameter estimation while maintaining alignment with the mathematical framework to ensure interpretability. The proposed model may allow the more robust and insightful analyses by leveraging the generalization power of deep learning and theoretical foundations of the mathematical models. © The Author(s) 2025.

关键词： Artificial neural networks COVID-19 Deep learning Graph convolutional neural network

Effective Dimension Aware Fractional-Order Stochastic Gradient Descent for Convex Optimization Problems

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arXiv 2025年

作者： Partohaghighi, Mohammad Marcia, Roummel Chen, YangQuan Electrical Engineering and Computer Science graduate program University of California Merced United States Department of Applied Mathematics University of California Merced MercedCA United States Lab Department of Mechanical Engineering School of Engineering University of California MercedCA95343 United States

Fractional-order stochastic gradient descent (FOSGD) leverages a fractional exponent to capture long-memory effects in optimization, yet its practical impact is often constrained by the difficulty of tuning and stabilizing this exponent. In this work, we introduce 2SED Fractional-Order Stochastic Gradient Descent (2SEDFOSGD), a novel method that synergistically combines the Two-Scale Effective Dimension (2SED) algorithm with FOSGD to automatically calibrate the fractional exponent in a data-driven manner. By continuously gauging model sensitivity and effective dimensionality, 2SED dynamically adjusts the exponent to curb erratic oscillations and enhance convergence rates. Theoretically, we demonstrate how this dimension-aware adaptation retains the benefits of fractional memory while averting the sluggish or unstable behaviors frequently observed in naive fractional SGD. Empirical evaluations across multiple benchmarks confirm that our 2SED-driven fractional exponent approach not only converges faster but also achieves more robust final performance, suggesting broad applicability for fractional-order methodologies in large-scale machine learning and related domains. © 2025, CC BY.

关键词： Convex optimization

Fairness Through Matching

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arXiv 2025年

作者： Kim, Kunwoong Kong, Insung Lee, Jongjin Chae, Minwoo Park, Sangchul Kim, Yongdai Department of Statistics Seoul National University Korea Republic of Department of Applied Mathematics University of Twente Netherlands Samsung Research Korea Republic of School of Law Seoul National University Korea Republic of Department of Statistics Interdisciplinary Program in Artificial Intelligence Seoul National University Korea Republic of Seoul National University Korea Republic of

Group fairness requires that different protected groups, characterized by a given sensitive attribute, receive equal outcomes overall. Typically, the level of group fairness is measured by the statistical gap between predictions from different protected groups. In this study, we reveal an implicit property of existing group fairness measures, which provides an insight into how the group-fair models behave. Then, we develop a new group-fair constraint based on this implicit property to learn group-fair models. To do so, we first introduce a notable theoretical observation: every group-fair model has an implicitly corresponding transport map between the input spaces of each protected group. Based on this observation, we introduce a new group fairness measure termed Matched Demographic Parity (MDP), which quantifies the averaged gap between predictions of two individuals (from different protected groups) matched by a given transport map. Then, we prove that any transport map can be used in MDP to learn group-fair models, and develop a novel algorithm called Fairness Through Matching (FTM)1, which learns a group-fair model using MDP constraint with an user-specified transport map. We specifically propose two favorable types of transport maps for MDP, based on the optimal transport theory, and discuss their advantages. Experiments reveal that FTM successfully trains group-fair models with certain desirable properties by choosing the transport map accordingly. © 2025, CC BY.

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A Traffic Evacuation Model for Enhancing Resilience During Railway Disruption

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arXiv 2025年

作者： Ge, Hangli Yang, Xiaojie Chen, Jinyu Flammini, Francesco Koshizuka, Noboru Interfaculty Initiative in Information Studies The University of Tokyo Tokyo Japan Graduate School of Interdisciplinary Information Studies The University of Tokyo Tokyo Japan Department of Mathematics and Computer Science Ulisse Dini University of Florence Florence Italy IDSIA USI-SUPSI University of Applied Sciences and Arts of Southern Switzerland Lugano Switzerland

This paper introduces a traffic evacuation model for railway disruptions to improve resilience. The research focuses on the problem of failure of several nodes or lines on the railway network topology. We proposed a holistic approach that integrates lines of various operator companies as well as external geographical features of the railway system. The optimized evacuation model was mathematically derived based on matrix computation using nonlinear programming. The model also takes into account the capacity of the surrounding evacuation stations, as well as the travel cost. Moreover, our model can flexibly simulate disruptions at multiple stations or any number of stations and lines, enhancing its applicability. We collected the large-scale railway network of the Greater Tokyo area for experimentation and evaluation. We simulated evacuation plans for several major stations, including Tokyo, Shinjuku, and Shibuya. The results indicate that the evacuation passenger flow (EPF) and the average travel time (ATT) during emergencies were optimized, staying within both the capacity limits of the targeted neighboring stations and the disruption recovery time. © 2025, CC BY.

关键词： Nonlinear programming

Emulating complex synapses using interlinked proton conductors

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Physical Review applied 2025年第1期23卷 014027-014027页

作者： Lifu Zhang Ji-An Li Yang Hu Jie Jiang Rongjie Lai Marcus K. Benna Jian Shi Department of Materials Science and Engineering Rensselaer Polytechnic Institute Troy New York 12180 USA Neurosciences Graduate Program University of California San Diego La Jolla California 92093 USA Department of Mathematics Purdue University West Lafayette Indiana 47907 USA Department of Neurobiology School of Biological Sciences University of California at San Diego La Jolla California 92093 USA Department of Physics Applied Physics and Astronomy Rensselaer Polytechnic Institute Troy New York 12180 USA

In terms of energy efficiency and computational speed, neuromorphic electronics based on nonvolatile memory devices are expected to be one of most promising hardware candidates for future artificial intelligence (AI). However, catastrophic forgetting, networks rapidly overwriting previously learned weights when learning new tasks, remains a pivotal obstacle in either digital or analog AI chips for unleashing the true power of brainlike computing. To address catastrophic forgetting in the context of online memory storage, a complex synapse model (the Benna-Fusi model) was proposed recently [M. K. Benna and S. Fusi, Nat. Neurosci. 19, 1697 (2016)], the synaptic weight and internal variables of which evolve following diffusion dynamics. In this work, by designing a proton transistor with a series of charge-diffusion-controlled storage components, we have experimentally realized the Benna-Fusi artificial complex synapse. Memory consolidation from coupled storage components is revealed by both numerical simulations and experimental observations. Different memory timescales for the complex synapse are engineered by the diffusion length of charge carriers and the capacity and number of coupled storage components. The advantages of the demonstrated complex synapse for both memory capacity and memory consolidation are revealed by neural network simulations of face-familiarity detection. Our experimental realization of the complex synapse suggests a promising approach to enhance memory capacity and to enable continual learning.

关键词： Nonvolatile storage

A SIZE-STRUCTURED MODEL FOR CANNIBALISM

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THEORETICAL POPULATION BIOLOGY 1992年第3期42卷 347-361页

作者： CUSHING, JM Department of Mathematics Interdisciplinary Program in Applied Mathematics Building 89 University of Arizona Tucson Arizona 85721 USA

A size-structured model for the dynamics of a cannibalistic population is derived under the assumption that cannibals (successfully) attack only smaller bodied victims, as is generally the case in the biological world. In addition to the resulting size-dependent death rate, the model incorporates the positive feedback mechanism resulting from the added resource energy obtained by the cannibal from the consumption of the victim. From the nonlinear partial integro-differential equation model, it is shown how to obtain a complete analysis of the global dynamics of the total population biomass. This analysis yields many dynamical features that have been attributed to cannibalism in the literature, including density self-regulation, a “life-boat strategy” phenomenon by which a population avoids extinction by practicing cannibalism under circumstances when it would otherwise go extinct, and multiple stable positive equilibrium states and hysteresis.

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