Related papers: The Lie Detector
Homogenisation empowers the efficient macroscale system level prediction of physical scenarios with intricate microscale structures. Here we develop an innovative powerful, rigorous and flexible framework for asymptotic homogenisation of…
Splitting methods are a widely used numerical scheme for solving convection-diffusion problems. However, they may lose stability in some situations, particularly when applied to convection-diffusion problems in the presence of an unbounded…
The physical sciences are replete with dynamical systems that require the resolution of a wide range of length and time scales. This presents significant computational challenges since direct numerical simulation requires discretization at…
Modern NLP systems exhibit a range of biases, which a growing literature on model debiasing attempts to correct. However current progress is hampered by a plurality of definitions of bias, means of quantification, and oftentimes vague…
The difference variational bicomplex, which is the natural setting for systems of difference equations, is constructed and used to examine the geometric and algebraic properties of various systems. Exactness of the bicomplex gives a…
Statistical models can involve implicitly defined quantities, such as solutions to nonlinear ordinary differential equations (ODEs), that unavoidably need to be numerically approximated in order to evaluate the model. The approximation…
Automated model discovery of partial differential equations (PDEs) usually considers a single experiment or dataset to infer the underlying governing equations. In practice, experiments have inherent natural variability in parameters,…
Many scientific problems focus on observed patterns of change or on how to design a system to achieve particular dynamics. Those problems often require fitting differential equation models to target trajectories. Fitting such models can be…
The goal of Science is to understand phenomena and systems in order to predict their development and gain control over them. In the scientific process of knowledge elaboration, a crucial role is played by models which, in the language of…
Theoretical background of continuous contractions of finite-dimensional Lie algebras is rigorously formulated and developed. In particular, known necessary criteria of contractions are collected and new criteria are proposed. A number of…
We show how to construct the optimum superstatistical dynamical model for a given experimentally measured time series. For this purpose we generalise the superstatistics concept and study a Langevin equation with a memory kernel whose…
Accurate comparisons between theoretical models and experimental data are critical for scientific progress. However, inferred physical model parameters can vary significantly with the chosen physics model, highlighting the importance of…
Modern numerical models are increasingly complex, opaque, and computationally expensive, yet frequently fail to predict even qualitative features of observed phenomena. We propose a new paradigm, Declarative Bespoke Modelling, in which the…
This paper presents the continuous and discrete variational formulations of simple thermodynamical systems whose configuration space is a (finite dimensional) Lie group. We follow the variational approach to nonequilibrium thermodynamics…
The process of calibrating computer models of natural phenomena is essential for applications in the physical sciences, where plenty of domain knowledge can be embedded into simulations and then calibrated against real observations. Current…
Numerical simulation of ordinary differential equations (ODEs) can be challenging when the system exhibits high accelerations and rapidly changing dynamics. Under these conditions the ODE solver often needs to take very small time steps in…
A systematic approach to finding variational approximation in an otherwise intractable non-conjugate model is to exploit the general principle of convex duality by minorizing the marginal likelihood that renders the problem tractable. While…
Form a pure mathematical point of view, common functional forms representing different physical phenomena can be defined. For example, rates of chemical reactions, diffusion and heat transfer are all governed by exponential-type…
As generative models continue to evolve, detecting AI-generated images remains a critical challenge. While effective detection methods exist, they often lack formal interpretability and may rely on implicit assumptions about fake content,…
Predicting outcomes and planning interactions with the physical world are long-standing goals for machine learning. A variety of such tasks involves continuous physical systems, which can be described by partial differential equations…