arXiv subjects

Guang Lin

Publications and source records attributed to Guang Lin.

At least 73 records · Page 4Linked to original sources

arXiv2025

A Review of AI-Driven Approaches for Nanoscale Heat Conduction and Radiation

Heat conduction and radiation are two of the three fundamental modes of heat transfer, playing a critical role in a wide range of scientific and engineering applications ranging from energy systems to materials science. However, traditional physics-based simulation methods for modeling these processes often suffer from prohibitive computational costs. In recent years, the rapid advancements in Artificial Intelligence (AI) and machine learning (ML) have demonstrated remarkable potential in the modeling of nanoscale heat conduction and radiation. This review presents a comprehensive overview of recent AI-driven developments in modeling heat conduction and radiation at the nanoscale. We first discuss the ML techniques for predicting phonon properties, including phonon dispersion and scattering rates, which are foundational for determining material thermal properties. Next, we explore the role of machine-learning interatomic potentials (MLIPs) in molecular dynamics simulations and their applications to bulk materials, low-dimensional systems, and interfacial transport. We then review the ML approaches for solving radiative heat transfer problems, focusing on data-driven solutions to Maxwell's equations and the radiative transfer equation. We further discuss the ML-accelerated inverse design of radiative energy devices, including optimization-based and generative model-based methods. Finally, we discuss open challenges and future directions, including data availability, model generalization, uncertainty quantification, and interpretability. Through this survey, we aim to provide a foundational understanding of how AI techniques are reshaping thermal science and guiding future research in nanoscale heat transfer.

cond-mat.mtrl-sci↗

arXiv2025

Finite Element Representation Network (FERN) for Operator Learning with a Localized Trainable Basis

We propose a finite-element local basis-based operator learning framework for solving partial differential equations (PDEs). Operator learning aims to approximate mappings from input functions to output functions, where the latter are typically represented using basis functions. While non-learnable bases reduce training costs, learnable bases offer greater flexibility but often require deep network architectures with a large number of trainable parameters. Existing approaches typically rely on deep global bases; however, many PDE solutions exhibit local behaviors such as shocks, sharp gradients, etc., and in parametrized PDE settings, these localized features may appear in different regions of the domain across different training and testing samples. Motivated by the use of local bases in finite element methods (FEM) for function approximation, we develop a shallow neural network architecture that constructs adaptive FEM bases. By adopting suitable activation functions, such as ReLU, the FEM bases can be assembled exactly within the network, introducing no additional approximation error in the basis construction process. This design enables the learning procedure to naturally mimic the adaptive refinement mechanism of FEM, allowing the network to discover basis functions tailored to intrinsic solution features such as shocks. The proposed learnable adaptive bases are then employed to represent the solution (output function) of the PDE. This framework reduces the number of trainable parameters while maintaining high approximation accuracy, effectively combining the adaptivity of FEM with the expressive power of operator learning. To evaluate performance, we validate the proposed method on seven families of PDEs with diverse characteristics, demonstrating its accuracy, efficiency, and robustness.

math.NA↗

arXiv2025

LLM Safety Alignment is Divergence Estimation in Disguise

We present a theoretical framework showing that popular LLM alignment methods, including RLHF and its variants, can be understood as divergence estimators between aligned (safe or preferred) and unaligned (harmful or less preferred) distributions. This perspective explains the emergence of separation in the latent space between safe and harmful prompts after alignment. As an application of our general divergence framework, we propose KLDO, a novel KL divergence-based alignment method, and empirically validate its effectiveness. We further show that using compliance-refusal datasets, rather than standard preference-based datasets, leads to stronger separation and improved safety alignment. Finally, to quantify the separation effect, we propose a distance-based metric in the prompt representation space, which also acts as a statistically significant indicator for model safety.

cs.LG↗

arXiv2025

Rethinking Langevin Thompson Sampling from A Stochastic Approximation Perspective

Most existing approximate Thompson Sampling (TS) algorithms for multi-armed bandits use Stochastic Gradient Langevin Dynamics (SGLD) or its variants in each round to sample from the posterior, relaxing the need for conjugacy assumptions between priors and reward distributions in vanilla TS. However, they often require approximating a different posterior distribution in different round of the bandit problem. This requires tricky, round-specific tuning of hyperparameters such as dynamic learning rates, causing challenges in both theoretical analysis and practical implementation. To alleviate this non-stationarity, we introduce TS-SA, which incorporates stochastic approximation (SA) within the TS framework. In each round, TS-SA constructs a posterior approximation only using the most recent reward(s), performs a Langevin Monte Carlo (LMC) update, and applies an SA step to average noisy proposals over time. This can be interpreted as approximating a stationary posterior target throughout the entire algorithm, which further yields a fixed step-size, a unified convergence analysis framework, and improved posterior estimates through temporal averaging. We establish near-optimal regret bounds for TS-SA, with a simplified and more intuitive theoretical analysis enabled by interpreting the entire algorithm as a simulation of a stationary SGLD process. Our empirical results demonstrate that even a single-step Langevin update with certain warm-up outperforms existing methods substantially on bandit tasks.

cs.LG↗

arXiv2025

BEKAN: Boundary condition-guaranteed evolutionary Kolmogorov-Arnold networks with radial basis functions for solving PDE problems

Deep learning has gained attention for solving PDEs, but the black-box nature of neural networks hinders precise enforcement of boundary conditions. To address this, we propose a boundary condition-guaranteed evolutionary Kolmogorov-Arnold Network (KAN) with radial basis functions (BEKAN). In BEKAN, we propose three distinct and combinable approaches for incorporating Dirichlet, periodic, and Neumann boundary conditions into the network. For Dirichlet problem, we use smooth and global Gaussian RBFs to construct univariate basis functions for approximating the solution and to encode boundary information at the activation level of the network. To handle periodic problems, we employ a periodic layer constructed from a set of sinusoidal functions to enforce the boundary conditions exactly. For a Neumann problem, we devise a least-squares formulation to guide the parameter evolution toward satisfying the Neumann condition. By virtue of the boundary-embedded RBFs, the periodic layer, and the evolutionary framework, we can perform accurate PDE simulations while rigorously enforcing boundary conditions. For demonstration, we conducted extensive numerical experiments on Dirichlet, Neumann, periodic, and mixed boundary value problems. The results indicate that BEKAN outperforms both multilayer perceptron (MLP) and B-splines KAN in terms of accuracy. In conclusion, the proposed approach enhances the capability of KANs in solving PDE problems while satisfying boundary conditions, thereby facilitating advancements in scientific computing and engineering applications.

cs.LG↗

arXiv2025

FourPhonon_GPU: A GPU-accelerated framework for calculating phonon scattering rates and thermal conductivity

Accurately predicting phonon scattering is crucial for understanding thermal transport properties. However, the computational cost of such calculations, especially for four-phonon scattering, can often be more prohibitive when large number of phonon branches and scattering processes are involved. In this work, we present FourPhonon_GPU, a GPU-accelerated framework for three-phonon and four-phonon scattering rate calculations based on the FourPhonon package. By leveraging OpenACC and adopting a heterogeneous CPU-GPU computing strategy, we efficiently offload massive, parallelizable tasks to the GPU while using the CPU for process enumeration and control-heavy operations. Our approach achieves over 25x acceleration for the scattering rate computation step and over 10x total runtime speedup without sacrificing accuracy. Benchmarking on various GPU architectures confirms the method's scalability and highlights the importance of aligning parallelization strategies with hardware capabilities. This work provides an efficient and accurate computational tool for phonon transport modeling and opens pathways for accelerated materials discovery.

cond-mat.mtrl-sci↗

arXiv2025

ProTDyn: a foundation Protein language model for Thermodynamics and Dynamics generation

Molecular dynamics (MD) simulation has long been the principal computational tool for exploring protein conformational landscapes and dynamics, but its application is limited by high computational cost. We present ProTDyn, a foundation protein language model that unifies conformational ensemble generation and multi-timescale dynamics modeling within a single framework. Unlike prior approaches that treat these tasks separately, ProTDyn allows flexible independent and identically distributed (i.i.d.) ensemble sampling and dynamic trajectory simulation. Across diverse protein systems, ProTDyn yields thermodynamically consistent ensembles, faithfully reproduces dynamical properties over multiple timescales, and generalizes to proteins beyond its training data. It offers a scalable and efficient alternative to conventional MD simulations.

physics.bio-ph↗

arXiv2025

Linear Spatial World Models Emerge in Large Language Models

Large language models (LLMs) have demonstrated emergent abilities across diverse tasks, raising the question of whether they acquire internal world models. In this work, we investigate whether LLMs implicitly encode linear spatial world models, which we define as linear representations of physical space and object configurations. We introduce a formal framework for spatial world models and assess whether such structure emerges in contextual embeddings. Using a synthetic dataset of object positions, we train probes to decode object positions and evaluate geometric consistency of the underlying space. We further conduct causal interventions to test whether these spatial representations are functionally used by the model. Our results provide empirical evidence that LLMs encode linear spatial world models.

cs.AI↗

arXiv2025

Exploring Non-Convex Discrete Energy Landscapes: An Efficient Langevin-Like Sampler with Replica Exchange

Gradient-based Discrete Samplers (GDSs) are effective for sampling discrete energy landscapes. However, they often stagnate in complex, non-convex settings. To improve exploration, we introduce the Discrete Replica EXchangE Langevin (DREXEL) sampler and its variant with Adjusted Metropolis (DREAM). These samplers use two GDSs at different temperatures and step sizes: one focuses on local exploitation, while the other explores broader energy landscapes. When energy differences are significant, sample swaps occur, which are determined by a mechanism tailored for discrete sampling to ensure detailed balance. Theoretically, we prove that the proposed samplers satisfy detailed balance and converge to the target distribution under mild conditions. Experiments across 2d synthetic simulations, sampling from Ising models and restricted Boltzmann machines, and training deep energy-based models further confirm their efficiency in exploring non-convex discrete energy landscapes.

cs.LG↗

arXiv2025

Large Language Model Sentinel: LLM Agent for Adversarial Purification

Over the past two years, the use of large language models (LLMs) has advanced rapidly. While these LLMs offer considerable convenience, they also raise security concerns, as LLMs are vulnerable to adversarial attacks by some well-designed textual perturbations. In this paper, we introduce a novel defense technique named Large LAnguage MOdel Sentinel (LLAMOS), which is designed to enhance the adversarial robustness of LLMs by purifying the adversarial textual examples before feeding them into the target LLM. Our method comprises two main components: a) Agent instruction, which can simulate a new agent for adversarial defense, altering minimal characters to maintain the original meaning of the sentence while defending against attacks; b) Defense guidance, which provides strategies for modifying clean or adversarial examples to ensure effective defense and accurate outputs from the target LLMs. Remarkably, the defense agent demonstrates robust defensive capabilities even without learning from adversarial examples. Additionally, we conduct an intriguing adversarial experiment where we develop two agents, one for defense and one for attack, and engage them in mutual confrontation. During the adversarial interactions, neither agent completely beat the other. Extensive experiments on both open-source and closed-source LLMs demonstrate that our method effectively defends against adversarial attacks, thereby enhancing adversarial robustness.

cs.CL↗

arXiv2025

Physics Informed Constrained Learning of Dynamics from Static Data

A physics-informed neural network (PINN) models the dynamics of a system by integrating the governing physical laws into the architecture of a neural network. By enforcing physical laws as constraints, PINN overcomes challenges with data scarsity and potentially high dimensionality. Existing PINN frameworks rely on fully observed time-course data, the acquisition of which could be prohibitive for many systems. In this study, we developed a new PINN learning paradigm, namely Constrained Learning, that enables the approximation of first-order derivatives or motions using non-time course or partially observed data. Computational principles and a general mathematical formulation of Constrained Learning were developed. We further introduced MPOCtrL (Message Passing Optimization-based Constrained Learning) an optimization approach tailored for the Constrained Learning framework that strives to balance the fitting of physical models and observed data. Its code is available at github link: https://github.com/ptdang1001/MPOCtrL Experiments on synthetic and real-world data demonstrated that MPOCtrL can effectively detect the nonlinear dependency between observed data and the underlying physical properties of the system. In particular, on the task of metabolic flux analysis, MPOCtrL outperforms all existing data-driven flux estimators.

cs.LG↗

arXiv2025

Conformalized-KANs: Uncertainty Quantification with Coverage Guarantees for Kolmogorov-Arnold Networks (KANs) in Scientific Machine Learning

This paper explores uncertainty quantification (UQ) methods in the context of Kolmogorov-Arnold Networks (KANs). We apply an ensemble approach to KANs to obtain a heuristic measure of UQ, enhancing interpretability and robustness in modeling complex functions. Building on this, we introduce Conformalized-KANs, which integrate conformal prediction, a distribution-free UQ technique, with KAN ensembles to generate calibrated prediction intervals with guaranteed coverage. Extensive numerical experiments are conducted to evaluate the effectiveness of these methods, focusing particularly on the robustness and accuracy of the prediction intervals under various hyperparameter settings. We show that the conformal KAN predictions can be applied to recent extensions of KANs, including Finite Basis KANs (FBKANs) and multifideilty KANs (MFKANs). The results demonstrate the potential of our approaches to improve the reliability and applicability of KANs in scientific machine learning.

cs.LG↗

arXiv2025

LLM Reasoning Engine: Specialized Training for Enhanced Mathematical Reasoning

Large Language Models (LLMs) have shown remarkable performance in various natural language processing tasks but face challenges in mathematical reasoning, where complex problem-solving requires both linguistic understanding and mathematical reasoning skills. Existing approaches to address this challenge often rely on ensemble methods and suffer from the problem of data scarcity in target domains. In this work, we present a novel method to enhance LLMs' capabilities in mathematical reasoning tasks. Motivated by the need to bridge this gap, our approach incorporates a question paraphrase strategy, which aims at diversifying the linguistic forms of mathematical questions to improve generalization. Additionally, specialized training objectives are employed to guide the model's learning process, focusing on enhancing its understanding of mathematical concepts and reasoning processes. We conduct experiments on four datasets using different LLMs, and demonstrate the effectiveness of our approach in improving LLMs' performance on mathematical reasoning tasks. Our findings underscore the significance of our methodology in the advancement of large language models and its potential implications for real-world applications that require mathematical reasoning abilities.

cs.CL↗

arXiv2025

Adversarial Guided Diffusion Models for Adversarial Purification

Diffusion model (DM) based adversarial purification (AP) has proven to be a powerful defense method that can remove adversarial perturbations and generate a purified example without threats. In principle, the pre-trained DMs can only ensure that purified examples conform to the same distribution of the training data, but it may inadvertently compromise the semantic information of input examples, leading to misclassification of purified examples. Recent advancements introduce guided diffusion techniques to preserve semantic information while removing the perturbations. However, these guidances often rely on distance measures between purified examples and diffused examples, which can also preserve perturbations in purified examples. To further unleash the robustness power of DM-based AP, we propose an adversarial guided diffusion model (AGDM) by introducing a novel adversarial guidance that contains sufficient semantic information but does not explicitly involve adversarial perturbations. The guidance is modeled by an auxiliary neural network obtained with adversarial training, considering the distance in the latent representations rather than at the pixel-level values. Extensive experiments are conducted on CIFAR-10, CIFAR-100 and ImageNet to demonstrate that our method is effective for simultaneously maintaining semantic information and removing the adversarial perturbations. In addition, comprehensive comparisons show that our method significantly enhances the robustness of existing DM-based AP, with an average robust accuracy improved by up to 7.30% on CIFAR-10.

cs.CV↗

arXiv2025

Coefficient-to-Basis Network: A Fine-Tunable Operator Learning Framework for Inverse Problems with Adaptive Discretizations and Theoretical Guarantees

We propose a Coefficient-to-Basis Network (C2BNet), a novel framework for solving inverse problems within the operator learning paradigm. C2BNet efficiently adapts to different discretizations through fine-tuning, using a pre-trained model to significantly reduce computational cost while maintaining high accuracy. Unlike traditional approaches that require retraining from scratch for new discretizations, our method enables seamless adaptation without sacrificing predictive performance. Furthermore, we establish theoretical approximation and generalization error bounds for C2BNet by exploiting low-dimensional structures in the underlying datasets. Our analysis demonstrates that C2BNet adapts to low-dimensional structures without relying on explicit encoding mechanisms, highlighting its robustness and efficiency. To validate our theoretical findings, we conducted extensive numerical experiments that showcase the superior performance of C2BNet on several inverse problems. The results confirm that C2BNet effectively balances computational efficiency and accuracy, making it a promising tool to solve inverse problems in scientific computing and engineering applications.

cs.LG↗

arXiv2025

Energy-Dissipative Evolutionary Kolmogorov-Arnold Networks for Complex PDE Systems

We introduce evolutionary Kolmogorov-Arnold Networks (EvoKAN), a novel framework for solving complex partial differential equations (PDEs). EvoKAN builds on Kolmogorov-Arnold Networks (KANs), where activation functions are spline based and trainable on each edge, offering localized flexibility across multiple scales. Rather than retraining the network repeatedly, EvoKAN encodes only the PDE's initial state during an initial learning phase. The network parameters then evolve numerically, governed by the same PDE, without any additional optimization. By treating these parameters as continuous functions in the relevant coordinates and updating them through time steps, EvoKAN can predict system trajectories over arbitrarily long horizons, a notable challenge for many conventional neural-network based methods. In addition, EvoKAN integrates the scalar auxiliary variable (SAV) method to guarantee unconditional energy stability and computational efficiency. At individual time step, SAV only needs to solve decoupled linear systems with constant coefficients, the implementation is significantly simplified. We test the proposed framework in several complex PDEs, including one dimensional and two dimensional Allen-Cahn equations and two dimensional Navier-Stokes equations. Numerical results show that EvoKAN solutions closely match analytical references and established numerical benchmarks, effectively capturing both phase-field phenomena (Allen-Cahn) and turbulent flows (Navier-Stokes).

math.NA↗

arXiv2025

Model-Free Adversarial Purification via Coarse-To-Fine Tensor Network Representation

Deep neural networks are known to be vulnerable to well-designed adversarial attacks. Although numerous defense strategies have been proposed, many are tailored to the specific attacks or tasks and often fail to generalize across diverse scenarios. In this paper, we propose Tensor Network Purification (TNP), a novel model-free adversarial purification method by a specially designed tensor network decomposition algorithm. TNP depends neither on the pre-trained generative model nor the specific dataset, resulting in strong robustness across diverse adversarial scenarios. To this end, the key challenge lies in relaxing Gaussian-noise assumptions of classical decompositions and accommodating the unknown distribution of adversarial perturbations. Unlike the low-rank representation of classical decompositions, TNP aims to reconstruct the unobserved clean examples from an adversarial example. Specifically, TNP leverages progressive downsampling and introduces a novel adversarial optimization objective to address the challenge of minimizing reconstruction error but without inadvertently restoring adversarial perturbations. Extensive experiments conducted on CIFAR-10, CIFAR-100, and ImageNet demonstrate that our method generalizes effectively across various norm threats, attack types, and tasks, providing a versatile and promising adversarial purification technique.

cs.LG↗

arXiv2024

Adversarial Autoencoders in Operator Learning

DeepONets and Koopman autoencoders are two prevalent neural operator architectures. These architectures are autoencoders. An adversarial addition to an autoencoder have improved performance of autoencoders in various areas of machine learning. In this paper, the use an adversarial addition for these two neural operator architectures is studied.

cs.LG↗