Related papers: Beyond Equilibrium: Non-Equilibrium Foundations Sh…

With the rise of computers, simulation models have emerged beside the more traditional statistical and mathematical models as a third pillar for ecological analysis. Broadly speaking, a simulation model is an algorithm, typically…

Dynamical systems theory has long provided a foundation for understanding evolving phenomena across scientific domains. Yet, the application of this theory to complex real-world systems remains challenging due to issues in mathematical…

Nonequilibrium statistical mechanics exhibit a variety of complex phenomena far from equilibrium. It inherits challenges of equilibrium, including accurately describing the joint distribution of a large number of configurations, and also…

Under many circumstances many soft and hard materials are present in a puzzling wealth of non-equilibrium amorphous states, whose properties are not stationary and depend on preparation. They are often summarized in unconventional "phase…

Generative AI models are increasingly being integrated into human task workflows, enabling the production of expressive content across a wide range of contexts. Unlike traditional human-AI design methods, the new approach to designing…

Large language model (LLM)-driven agents are emerging as a powerful new paradigm for solving complex problems. Despite the empirical success of these practices, a theoretical framework to understand and unify their macroscopic dynamics…

Calculations of nonequilibrium processes become increasingly feasable in quantum field theory from first principles. There has been important progress in our analytical understanding based on 2PI generating functionals. In addition, for the…

Generative AI research increasingly confronts a shared problem: systems must sustain yet govern their own generative activity when uncertainty is high, evidence is missing, or context is insufficient. This position paper argues that…

Nonequilibrium thermodynamics formalism is proposed to derive the flux of grainy (bubbles-containing) matter, emerging in a nucleation growth process. Some power and non-power limits, due to the applied potential as well as owing to basic…

We consider the problem of forecasting complex, nonlinear space-time processes when observations provide only partial information of on the system's state. We propose a natural data-driven framework, where the system's dynamics are modelled…

We discuss an approach to mathematically modelling systems made of objects that are coupled together, using generative models of the dependence relationships between states (or trajectories) of the things comprising such systems. This broad…

By generalizing a class of models recently introduced to account for protracted transients in biological systems, we identify a novel mechanism for hyperuniformity. In this model, competition of particles over a shared resource guides the…

Generative models producing images have enormous potential to advance discoveries across scientific fields and require metrics capable of quantifying the high dimensional output. We propose that astrophysics data, such as galaxy images, can…

We study the problem of modeling a non-linear dynamical system when given a time series by deriving equations directly from the data. Despite the fact that time series data are given as input, models for dynamics and estimation algorithms…

The rapid advancement of embodied intelligence and world models has intensified efforts to integrate physical laws into AI systems, yet physical perception and symbolic physics reasoning have developed along separate trajectories without a…

Generative models realized with machine learning techniques are powerful tools to infer complex and unknown data distributions from a finite number of training samples in order to produce new synthetic data. Diffusion models are an emerging…

We give a novel formal theoretical framework for unsupervised learning with two distinctive characteristics. First, it does not assume any generative model and based on a worst-case performance metric. Second, it is comparative, namely…

This study presents the approach to analyzing the evolution of an arbitrary complex system whose behavior is characterized by a set of different time-dependent factors. The key requirement for these factors is only that they must contain an…

Generative AI has achieved remarkable empirical success, but from the perspective of statistics it often remains opaque: its predictions may be accurate, yet the underlying mechanism is difficult to interpret, analyze, and trust. This book…

Discovering governing equations from data is crucial for understanding complex systems in many diverse fields from science to engineering. Yet, there still is a lack of versatile computational toolbox to deal with this long standing…