arXiv subjects

Chun Liu

Publications and source records attributed to Chun Liu.

At least 19 recordsLinked to original sources

arXiv2026

Stability in Training PINNs for Stiff PDEs: Why Initial Conditions Matter

Training physics-informed neural networks (PINNs) on stiff, time-dependent PDEs remains a fundamental challenge due to optimization instabilities and gradient pathologies. Through a series of rigorous ablation studies and Neural Tangent Kernel (NTK) analysis, we identify that the exact enforcement of initial conditions (ICs) is a decisive factor in stabilizing the training landscape. We present the first systematic ablation of two core strategies: hard initial-condition constrained transformation and self-adaptive loss weighting. Our findings demonstrate that embedding ICs directly into the network architecture provides an implicit time-marching effect, effectively reducing spectral bias and enabling the solution of highly stiff benchmarks, including sharp transitions and high-frequency coupled systems, primarily under periodic boundary conditions, with a Dirichlet extension reported as an additional robustness check. This work provides a scalable framework for developing reliable and physically-consistent neural solvers for complex mechanical systems.

math.NA↗

arXiv2026

Thermodynamically Consistent Modeling of ATP-Driven Cross-Bridge Dynamics in Muscle Contraction

Muscle contraction is a prototypical multiscale chemomechanical process in which ATP hydrolysis at the molecular level drives force generation and mechanical work at larger scales. A central challenge is to incorporate the free energy supplied by ATP hydrolysis into a mechanical cross-bridge model in a way that is thermodynamically consistent and connects microscopic motor cycling to macroscopic force generation. Here we use the Energetic Variational Approach (EnVarA) to combine Hill's cycle-affinity viewpoint with Huxley's sliding-filament mechanics in a single thermodynamically consistent framework. We formulate a three-state Fokker--Planck--jump description for cross-bridge densities evolving on state-dependent free-energy landscapes, and treat ATP, ADP, and Pi as reacting and diffusing chemical species that share the same free-energy functional as the cross-bridge densities. ATP hydrolysis enters the model through local detailed balance, which biases the transition rates. Filament sliding velocity is incorporated as a convective transport term in the Fokker--Planck dynamics, so mechanical power output is defined directly from the energy balance law. Under chemostatted conditions and a fast-equilibration assumption for the two attached states, the model reduces to a closed two-state molecular motor description; in a further small-diffusion limit, this reduction recovers a Huxley-type transport-reaction equation whose effective attachment and detachment rates are derived from the underlying three-state cycle rather than prescribed phenomenologically, with their strain, ATP, and phosphate dependence fixed by the energy landscapes and local detailed balance. We calibrate the reduced model against cross-bridge-level observables and show that it reproduces key velocity-dependent trends and yields a Hill-like force--velocity relation comparable to established cross-bridge models.

cond-mat.soft↗

arXiv2026

Global Finite-Energy Weak Solutions and Sharp Entropy Decay for a Poisson-Nernst-Planck System with Interspecies Drag and Steric Effects

We derive and analyze a binary Poisson-Nernst-Planck system with steric interactions and interspecies drag through the energetic variational approach. The steric effects are incorporated into the free energy, while the drag mechanism enters the dissipation functional; eliminating the transport velocities yields a non-diagonal, concentration-dependent Onsager mobility and an entropy-production structure that is not coercive in the standard $L^2(0,T;H^1)$ sense. For the resulting drag-modified steric PNP system, we prove the existence of global finite-energy weak solutions using an entropy-variable approximation, weighted gradient estimates, and a vacuum-compatible square-root formulation of the weighted entropy gradients. In the pure Neumann equal-mass setting, we establish a sublevel entropy-entropy production inequality, obtain exponential relaxation for approximation-generated weak solutions, and identify the sharp small-sublevel limit of the optimal entropy-production constant through an explicit linearized formula involving the drag mobility, steric Hessian, Poisson coupling, and Neumann spectrum. We further show that the same linearized constant governs the local nonlinear relaxation of sufficiently small strong perturbations of the homogeneous equilibrium. Finally, we discuss the rank-one steric limit and clarify the role of the positive definiteness of the steric matrix in the finite-energy compactness theory.

math.AP↗

arXiv2026

A Gauge Model for Quasi-Dirac Neutrinos

In a model with $L_μ - L_τ$ Abelian gauge symmetry, anomaly-free chiral fermions, which are Standard Model singlets, are introduced as the origin of right-handed neutrinos. This $\mathsf{U} (1)$ symmetry keeps the right-handed neutrinos Majorana massless. Tiny nonvanishing Dirac masses of neutrinos are due to higher-dimensional operators with natural coupling constants. After gauge symmetry breaking, a quasi-Dirac neutrino scenario naturally appears, and realistic neutrino physics can be produced. Phenomenological and cosmological aspects of the model are discussed.

hep-ph↗

arXiv2026

Learning the Energy Landscapes of Dynamical Systems via Energetic Variational Optimal Transport under Data Quantity--Quality Trade-offs

Dynamic optimal transport unifies optimal transport, fluid mechanics, and gradient-flow theory within a continuous dynamical framework, offering a geometry-aware language for applications across physics, biology, and machine learning. However, conventional formulations cast it as a constrained optimization problem that must explicitly satisfy the continuity equation, hindering the reconstruction of the underlying dynamics directly from data. We propose the energetic variational method for dynamic optimal transport (EVMDOT), which reformulates it within an energetic variational framework by combining the flow map, the least action principle, and the maximum dissipation principle. The flow map recasts the constrained problem as an unconstrained one by automatically enforcing the continuity equation, while the balance between the conservative and dissipative forces determines the velocity field. Applied to the Fokker--Planck equation, the EVMDOT reconstructs both the energy landscape and the Waddington landscape directly from time-series density data. Through numerical experiments, we reveal that the EVMDOT achieves an intrinsic balance between data quantity and data quality: a sufficient data quantity compensates for limited data quality, making the reconstruction robust to the choice of the observation window. We further apply the EVMDOT to the Alzheimer's Disease Neuroimaging Initiative (ADNI) dataset to infer the potential landscape of amyloid-$β$ and tau, revealing two wells corresponding to the cognitively normal and Alzheimer's disease stages and the transition pathway between them.

math.DS↗

arXiv2026

A Deterministic Sampling Method via Maximum Mean Discrepancy Flow with Adaptive Kernel

We propose a novel deterministic sampling method, EVI-MMD, to approximate a target distribution $ρ^*$ by minimizing the kernel discrepancy, also known as the Maximum Mean Discrepancy (MMD). Leveraging the energetic variational inference framework (Wang et al., 2021), we transform the MMD minimization problem into solving a dynamic system of Ordinary Differential Equations (ODEs) for particles. The implicit Euler scheme is employed to solve the ODE system, leading to a proximal minimization problem at each iteration, which is efficiently addressed using optimization algorithms such as L-BFGS. A key innovation of our method is a dynamic bandwidth selection strategy for the Gaussian kernel, which, although heuristic at this stage, represents a meaningful step toward addressing a long-standing challenge in kernel-based methods. Comprehensive numerical experiments demonstrate that this adaptive bandwidth significantly enhances the performance of EVI-MMD. We apply the EVI-MMD algorithm to two types of sampling problems: (1) when the target distribution is fully specified by a density function, and (2) the ``two-sample problem,'' where only training data are available. In the latter case, EVI-MMD serves as a generative model, producing new samples that faithfully replicate the distribution of the training data. With carefully tuned parameters, EVI-MMD outperforms several existing methods in both scenarios.

stat.ML↗

arXiv2026

Robust Investment-Driven Insurance Pricing and Liquidity Management

This paper develops a dynamic equilibrium model of the insurance market that jointly characterizes insurers' underwriting, investment, recapitalization, and dividend policies under model uncertainty and financial frictions. Competitive insurers maximize shareholder value under a subjective worst-case probability measure, giving rise to liquidity-driven underwriting cycles and flight-to-quality behavior. Model uncertainty acts as an informational friction on insurers' risk-taking behavior and helps regularize a finite-barrier verification system in settings with external financial investment opportunities. We further show that robustness concerns do not eliminate the investment-hedging channel in insurance pricing: when underwriting surplus and financial returns are sufficiently negatively correlated, the hedging value of financial investment can be passed through to policyholders, leading to lower insurance prices and, in high-capacity states, negative equilibrium loadings. Thus, underwriting losses may arise endogenously even when insurers price rationally under model uncertainty, rather than necessarily reflecting mispricing or irrational underwriting behavior.

q-fin.RM↗

arXiv2026

Accelerating Particle-based Energetic Variational Inference

In this work, we propose a new particle-based variational inference (ParVI) method for accelerating the Energetic Variational Inference with Implicit scheme (EVI-Im) introduced in Ref. \cite{wang2021particle}. Inspired by energy quadratization (EQ) and operator splitting techniques for gradient flows, the proposed method efficiently drives particles towards the target distribution, while retaining a meaningful stability mechanism. Unlike EVI-Im, which employs the implicit Euler method to solve variational-preserving particle dynamics obtained from a "discretization-then-variation" approach for minimizing the Kullback--Leibler divergence, the proposed algorithm avoids repeated evaluation of inter-particle interaction terms within each time step, significantly reducing computational cost. The framework is also extensible to other gradient-based sampling techniques. Through several numerical experiments, we demonstrate that the proposed method achieves competitive performance compared with existing ParVI approaches, while offering advantages in efficiency and robustness in certain regimes.

stat.ML↗

arXiv2026

Efficient Verification of Neural Control Barrier Functions with Smooth Nonlinear Activations

Formal verification of neural control barrier functions (NCBFs) remains challenging, especially for neural networks with nonlinear activations like $\tanh$. Existing CROWN-based methods rely on conservative linear relaxations for Jacobian bounds, limiting scalability. We propose LightCROWN, which computes tighter Jacobian bounds by exploiting the analytical properties of activation functions. Experiments on nonlinear control systems including the inverted pendulum, Dubins car, and planar quadrotor demonstrate that LightCROWN improves verification success rates up to 100\%, while enhancing speed and scalability. Our approach provides a generalizable improvement for CROWN-based frameworks, enabling more efficient verification of complex NCBFs. The code can be found at github.com/Autonomous-Systems-and-Control-Lab/verify-neural-CBF.

cs.LG↗

arXiv2026

Structure-Aware Variational Learning of a Class of Generalized Diffusions

Learning the underlying potential energy of stochastic gradient systems from partial and noisy observations is a fundamental problem arising in physics, chemistry, and data-driven modeling. Classical approaches often rely on direct regression of governing equations or velocity fields, which can be sensitive to noise and external perturbations and may fail when observations are incomplete. In this work, we propose a structure-aware, energy-based learning framework for inferring unknown potential functions in generalized diffusion processes, grounded in the energetic variational approach. Starting from the energy-dissipation law associated with the Fokker-Planck equation, we construct loss functions based on the De Giorgi dissipation functional, which consistently couple the free energy and the dissipation mechanism of the system. This formulation avoids explicit enforcement of the governing partial differential equation and preserves the underlying variational structure of the dynamics. Through numerical experiments in one, two, and three dimensions, we demonstrate that the proposed energy-based loss exhibits enhanced robustness with respect to observation time, noise level, and the diversity and amount of available training data. These results highlight the effectiveness of energy-dissipation principles as a reliable foundation for learning stochastic diffusion dynamics from data.

cs.LG↗

arXiv2026

Finite Difference Approximation with ADI Scheme for Two-dimensional Keller-Segel Equations

Keller-Segel systems are a set of nonlinear partial differential equations used to model chemotaxis in biology. In this paper, we propose two alternating direction implicit (ADI) schemes to solve the 2D Keller-Segel systems directly with minimal computational cost, while preserving positivity, energy dissipation law and mass conservation. One scheme unconditionally preserves positivity, while the other does so conditionally. Both schemes achieve second-order accuracy in space, with the former being first-order accuracy in time and the latter second-order accuracy in time. Besides, the former scheme preserves the energy dissipation law asymptotically. We validate these results through numerical experiments, and also compare the efficiency of our schemes with the standard five-point scheme, demonstrating that our approaches effectively reduce computational costs.

math.NA↗

arXiv2026

Learning Generalized Diffusions using an Energetic Variational Approach

Extracting governing physical laws from computational or experimental data is crucial across various fields such as fluid dynamics and plasma physics. Many of those physical laws are dissipative due to fluid viscosity or plasma collisions. For such a dissipative physical system, we propose a framework to learn the corresponding laws of the systems based on their energy-dissipation laws, assuming either continuous data (probability density) or discrete data (particles) are available. Our methods offer several key advantages, including their robustness to corrupted/noisy observations, their easy extension to more complex physical systems, and the potential to address higher-dimensional systems. We validate our approaches through representative numerical examples and carefully investigate the impacts of data quantity and data property on model discovery.

physics.comp-ph↗

arXiv2026

When Noise Lowers The Loss: Rethinking Likelihood-Based Evaluation in Music Large Language Models

The rise of music large language models (LLMs) demands robust methods of evaluating output quality, especially in distinguishing high-quality compositions from "garbage music". Curiously, we observe that the standard cross-entropy loss -- a core training metric -- often decrease when models encounter systematically corrupted music, undermining its validity as a standalone quality indicator. To investigate this paradox, we introduce noise injection experiment, where controlled noise signal of varying lengths are injected into musical contexts. We hypothesize that a model's loss reacting positively to these perturbations, specifically a sharp increase ("Peak" area) for short injection, can serve as a proxy for its ability to discern musical integrity. Experiments with MusicGen models in the audio waveform domain confirm that Music LLMs respond more strongly to local, texture-level disruptions than to global semantic corruption. Beyond exposing this bias, our results highlight a new principle: the shape of the loss curve -- rather than its absolute value -- encodes critical information about the quality of the generated content (i.e., model behavior). We envision this profile-based evaluation as a label-free, model-intrinsic framework for assessing musical quality -- opening the door to more principled training objectives and sharper benchmarks.

cs.SD↗

arXiv2026

A Schrödinger-Based Dispersive Regularization Approach for Numerical Simulation of One-Dimensional Shallow Water Equations

We propose a novel dispersive regularization framework for the numerical simulation of the one-dimensional shallow water equations (SWE). The classical hyperbolic system is regularized by a third-order dispersive term in the momentum equation, which renders the system equivalent, via the Madelung transform, to a defocusing cubic nonlinear Schrödinger equation with a drift term induced by bottom topography. Instead of solving the shallow water equations directly, we solve the associated Schrödinger equation and recover the hydrodynamic variables through a simple postprocessing procedure. This approach transforms the original nonlinear hyperbolic system into a semilinear complex-valued equation, which can be efficiently approximated using a Strang time-splitting method combined with a spectral element discretization in space. Numerical experiments demonstrate that, in subcritical regimes without shock formation, the Schrödinger regularization provides an $O(\varepsilon)$ approximation to the classical shallow water solution, where $\varepsilon$ denotes the regularization parameter. Importantly, we observe that this convergence behavior persists even in the presence of moving wetting--drying interfaces, where vacuum states emerge and standard shallow water solvers often encounter difficulties. These results suggest that the Schrödinger-based formulation offers a robust and promising alternative framework for the numerical simulation of shallow water flows with dry states.

math.NA↗

arXiv2025

An Asymptotic Approach for Modeling Multiscale Complex Fluids at the Fast Relaxation Limit

We present a new asymptotic strategy for general micro-macro models which analyze complex viscoelastic fluids governed by coupled multiscale dynamics. In such models, the elastic stress appearing in the macroscopic continuum equation is derived from the microscopic kinetic theory, which makes direct numerical simulations computationally expensive. To address this challenge, we introduce a formal asymptotic scheme that expands the density function around an equilibrium distribution, thereby reducing the high computational cost associated with the fully coupled microscopic processes while still maintaining the dynamic microscopic feedback in explicit expressions. The proposed asymptotic expansion is based on a detailed physical scaling law which characterizes the multiscale balance at the fast relaxation limit of the microscopic state. An asymptotic closure model for the macroscopic fluid equation is then derived according to the explicit asymptotic density expansion. Furthermore, the resulting closure model preserves the energy-dissipation law inherited from the original fully coupled multiscale system. Numerical experiments are performed to validate the asymptotic density formula and the corresponding flow velocity equations in several micro-macro models. This new asymptotic strategy offers a promising approach for efficient computations of a wide range of multiscale complex fluids.

math-ph↗

arXiv2025

Elastic scattering problems by penetrable obstacles with embedded objects

This paper considers 3-D elastic scattering problems by penetrable obstacles with embedded objects. The well-posedness of transmission problem is proved by employing integral equation method. Then the Inverse Problems , which is to recover the obstacle by the far-field pattern measurement, is considered. It is shown that the inhomogeneous penetrable obstacle can be uniquely determined from the far-field pattern at a fixed frequency.

math.AP↗

arXiv2025

Unified Learning of the Profile Function in Discrete Keller-Segel Models

We propose a unified learning framework for identifying the profile function in discrete Keller-Segel equations, which are widely used mathematical models for understanding chemotaxis. Training data are obtained via either a rigorously developed particle method designed for stable simulation of high-dimensional Keller-Segel systems, or stochastic differential equations approximating the continuous Keller-Segel PDE. Our approach addresses key challenges, including data instability in dimensions higher than two and the accurate capture of singular behavior in the profile function. Additionally, we introduce an adaptive learning strategy to enhance performance. Extensive numerical experiments are presented to validate the effectiveness of our method.

math.NA↗

arXiv2025

Generating Transferrable Adversarial Examples via Local Mixing and Logits Optimization for Remote Sensing Object Recognition

Deep Neural Networks (DNNs) are vulnerable to adversarial attacks, posing significant security threats to their deployment in remote sensing applications. Research on adversarial attacks not only reveals model vulnerabilities but also provides critical insights for enhancing robustness. Although current mixing-based strategies have been proposed to increase the transferability of adversarial examples, they either perform global blending or directly exchange a region in the images, which may destroy global semantic features and mislead the optimization of adversarial examples. Furthermore, their reliance on cross-entropy loss for perturbation optimization leads to gradient diminishing during iterative updates, compromising adversarial example quality. To address these limitations, we focus on non-targeted attacks and propose a novel framework via local mixing and logits optimization. First, we present a local mixing strategy to generate diverse yet semantically consistent inputs. Different from MixUp, which globally blends two images, and MixCut, which stitches images together, our method merely blends local regions to preserve global semantic information. Second, we adapt the logit loss from targeted attacks to non-targeted scenarios, mitigating the gradient vanishing problem of cross-entropy loss. Third, a perturbation smoothing loss is applied to suppress high-frequency noise and enhance transferability. Extensive experiments on FGSCR-42 and MTARSI datasets demonstrate superior performance over 12 state-of-the-art methods across 6 surrogate models. Notably, with ResNet as the surrogate on MTARSI, our method achieves a 17.28% average improvement in black-box attack success rate.

cs.CV↗