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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 properties on model discovery. 

In this paper, we derive a thermodynamically consistent nonisothermal di!use interface model for phase transition and interface evolution involving heat transfer. This model is constructed by integrating concepts from classical irreversible thermodynamics and the energetic variational approach. By making specific assumptions about the kinematics of the temperature, we derive a nonisothermal Allen–Cahn equation. Through both asymptotic analysis and numerical simulations, we demonstrate that in the sharp interface limit, the nonisothermal Allen–Cahn equation converges to a two-phase nonlinear Stefan type problem, under a certain scaling of the melting/freezing energy. In this regime, the motion of the liquid-solid interface and the temperature interface coincides and is governed by the mean curvature flow, at least for a short time. The result provides a justification for the classical Stefan problem within a certain physical regime. 

We propose a new continuum model for random genetic drift by employing a dynamic boundary condition approach. The model can be viewed as a regularized version of the Kimura equation and admits a continuous solution. We establish existence and uniqueness of a strong solution to the regularized system. Numerical experiments illustrate that, for sufficiently small regularization parameters, the model can capture key phenomena of the original Kimura equation, such as gene fixation and conservation of the first moment. 

In this paper, we explore pattern formation in a four-species variational Gary-Scott model, which includes all reverse reactions and introduces a virtual species to describe the birth–death process in the classical Gray-Scott model. This modification transforms the classical Gray-Scott model into a thermodynamically consistent closed system. The classical two-species Gray-Scott model can be viewed as a subsystem of the variational model in the limiting case when the small parameter ε, related to the reaction rate of the reverse reactions, approaches zero. We numerically explore pattern formation in this physically more complete Gray-Scott model in one spatial dimension, using non-uniform steady states of the classical model as initial conditions. By decreasing ε, we observed that the stationary patterns in the classical Gray-Scott model can be stabilized as the transient states in the variational model for a significantly small ε. Additionally, the variational model admits oscillating and traveling wave-like patterns for small ε. The persistent time of these patterns is on the order of O(1/ε). We also analyze the energy stability of two uniform steady states in the variational Gary-Scott model for fixed. Although both states are stable in a certain sense, the gradient flow type dynamics of the variational model exhibit a selection effect based on the initial conditions, with pattern formation occurring only if the initial condition does not converge to the boundary steady state, which corresponds to the trivial uniform steady state in the classical Gray-Scott model. 

AI-synthesized voice technology has the potential to create realistic human voices for beneficial applications, but it can also be misused for malicious purposes. While existing AI-synthesized voice detection models excel in intra-domain evaluation, they face challenges in generalizing across different domains, potentially becoming obsolete as new voice generators emerge. Current solutions use diverse data and advanced machine learning techniques (e.g., domain-invariant representation, self-supervised learning), but are limited by predefined vocoders and sensitivity to factors like background noise and speaker identity. In this work, we introduce an innovative disentanglement framework aimed at extracting domain-agnostic artifact features related to vocoders. Utilizing these features, we enhance model learning in a flat loss landscape, enabling escape from suboptimal solutions and improving generalization. Extensive experiments on benchmarks show our approach outperforms state-of-the-art methods, achieving up to 5.12% improvement in the equal error rate metric in intra-domain and 7.59% in cross-domain evaluations.