Related papers: Learning dominant physical processes with data-dri…
The climate system is a forced, dissipative, nonlinear, complex and heterogeneous system that is out of thermodynamic equilibrium. The system exhibits natural variability on many scales of motion, in time as well as space, and it is subject…
We present a machine learning based approach to address the study of transport processes, ubiquitous in continuous mechanics, with particular attention to those phenomena ruled by complex micro-physics, impractical to theoretical…
Mathematical models are vital to the field of metrology, playing a key role in the derivation of measurement results and the calculation of uncertainties from measurement data, informed by an understanding of the measurement process. These…
The identification of a nonlinear dynamic model is an open topic in control theory, especially from sparse input-output measurements. A fundamental challenge of this problem is that very few to zero prior knowledge is available on both the…
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…
Dynamical systems are found in innumerable forms across the physical and biological sciences, yet all these systems fall naturally into universal equivalence classes: conservative or dissipative, stable or unstable, compressible or…
In this paper we explore the performance of deep hidden physics model (M. Raissi 2018) for autonomous systems. These systems are described by set of ordinary differential equations which do not explicitly depend on time. Such systems can be…
We present a data-driven modeling strategy to overcome improperly modeled dynamics for systems exhibiting complex spatio-temporal behaviors. We propose a Deep Learning framework to resolve the differences between the true dynamics of the…
We present a novel reformulation of balanced truncation, a classical model reduction method. The principal innovation that we introduce comes through the use of system response data that has been either measured or computed, without…
Nonlinear models and optimization methods have successfully tackled a rapidly growing set of problems in recent years. Indeed, a relatively small toolbox of such models and methods can provide sufficient performance across a large landscape…
Large scale dynamical systems (e.g. many nonlinear coupled differential equations) can often be summarized in terms of only a few state variables (a few equations), a trait that reduces complexity and facilitates exploration of behavioral…
Turbulence modeling is a critical component in numerical simulations of industrial flows based on Reynolds-averaged Navier-Stokes (RANS) equations. However, after decades of efforts in the turbulence modeling community, universally…
In numerical modeling of the Earth System, many processes remain unknown or ill represented (let us quote sub-grid processes, the dependence to unknown latent variables or the non-inclusion of complex dynamics in numerical models) but…
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…
Design, control, and estimation for dynamic systems require accurate and analytically tractable models. However, modern engineered systems contain components that are described with heterogeneous modeling paradigms, as well as subsystems…
Laser-plasma physics has developed rapidly over the past few decades as high-power lasers have become both increasingly powerful and more widely available. Early experimental and numerical research in this field was restricted to…
Restrictive phenomenological assumptions represent a major roadblock for the development of accurate subgrid-scale models of fluid turbulence. Specifically, these assumptions limit a model's ability to describe key quantities of interest,…
As data-driven modeling of physical dynamical systems becomes more prevalent, a new challenge is emerging: making these models more compatible and aligned with existing human knowledge. AI-driven scientific modeling processes typically…
How does the brain predict physical outcomes while acting in the world? Machine learning world models compress visual input into latent spaces, discarding the spatial structure that characterizes sensory cortex. We propose isomorphic world…
The operation of power systems is affected by diverse technical, economic and social factors. Social behaviour determines load patterns, electricity markets regulate the generation and weather-dependent renewables introduce power…