Related papers: Hypothesis-driven construction of mesoscopic dynam…
We develop a monadic framework formalising an operational notion of dynamics, seen as the setting and evolution of initial value problems, in general physical theories. We identify in the Eilenberg-Moore category the natural environment for…
Dynamical systems theory provides powerful methods to extract effective macroscopic dynamics from complex systems with slow modes and fast modes. Here we derive and theoretically support a macroscopic, spatially discrete, model for a class…
We develop a mesoscopic modeling framework for diffusion in a crowded environment, particularly targeting applications in the modeling of living cells. Through homogenization techniques we effectively coarse-grain a detailed microscopic…
In this paper physical multi-scale processes governed by their own principles for evolution or equilibrium on each scale are coupled by matching the stored and dissipated energy, in line with the Hill-Mandel principle. In our view the…
Mathematical descriptions of dynamical systems are deeply rooted in topological spaces defined by non-Euclidean geometry. This paper proposes leveraging structure-rich geometric spaces for machine learning to achieve structural…
We introduce a mesoscopic three-dimensional Lattice Boltzmann Model which attempts to mimick the physical features associated with cage effects in dynamically heterogeneous fluids. To this purpose, we extend the standard Lattice Boltzmann…
In this paper, we propose a systematic way of liquid crystal modeling to build connection between microscopic theory and macroscopic theory. A new Q-tensor theory based on Onsager's molecular theory which leads to liquid crystals with…
We introduce a flexible, scalable Bayesian inference framework for nonlinear dynamical systems characterised by distinct and hierarchical variability at the individual, group, and population levels. Our model class is a generalisation of…
In the mechanics of inviscid conservative fluids, it is classical to generate the equations of dynamics by formulating with adequate variables, that the pressure integral calculated in the time-space domain corresponding to the motion of…
We introduce and analyze a model for the transport of particles or energy in extended lattice systems. The dynamics of the model acts on a discrete phase space at discrete times but has nonetheless some of the characteristic properties of…
In this paper, we present a Bayesian view on model-based reinforcement learning. We use expert knowledge to impose structure on the transition model and present an efficient learning scheme based on variational inference. This scheme is…
Quantum electrodynamics under conditions of distinguishability of interacting matter entities, and of controlled actions and back-actions between them, is considered. Such "mesoscopic quantum electrodynamics" is shown to share its dynamical…
Data-based discovery of effective, coarse-grained (CG) models of high-dimensional dynamical systems presents a unique challenge in computational physics and particularly in the context of multiscale problems. The present paper offers a…
We review and extend existing frameworks on modeling to develop a new framework that describes model-based reasoning in upper-division physics labs. Constructing and using models are core scientific practices that have gained significant…
Pedestrian crowds encompass a complex interplay of intentional movements aimed at reaching specific destinations, fluctuations due to personal and interpersonal variability, and interactions with each other and the environment. Previous…
This paper introduces a novel multi-stage decision-making model that integrates hypothesis testing and dynamic programming algorithms to address complex decision-making scenarios.Initially,we develop a sampling inspection scheme that…
In conventional ODE modelling coefficients of an equation driving the system state forward in time are estimated. However, for many complex systems it is practically impossible to determine the equations or interactions governing the…
This book presents a methodology and philosophy of empirical science based on large scale lossless data compression. In this view a theory is scientific if it can be used to build a data compression program, and it is valuable if it can…
Causal representation learning promises to extend causal models to hidden causal variables from raw entangled measurements. However, most progress has focused on proving identifiability results in different settings, and we are not aware of…
We consider a class of sequential decision-making problems under uncertainty that can encompass various types of supervised learning concepts. These problems have a completely observed state process and a partially observed modulation…