Related papers: Hypothesis-driven construction of mesoscopic dynam…
We propose a systematic method for learning stable and physically interpretable dynamical models using sampled trajectory data from physical processes based on a generalized Onsager principle. The learned dynamics are autonomous ordinary…
Many systems in physics, engineering, and biology exhibit multiscale stochastic dynamics, where low-dimensional slow variables evolve under the influence of high-dimensional fast processes. In practice, observations are often limited to a…
When human operators of cyber-physical systems encounter surprising behavior, they often consider multiple hypotheses that might explain it. In some cases, taking information-gathering actions such as additional measurements or control…
One of the most exciting applications of artificial intelligence (AI) is automated scientific discovery based on previously amassed data, coupled with restrictions provided by known physical principles, including symmetries and conservation…
We derive a mesoscopic modeling and simulation technique that is very close to the technique known as dissipative particle dynamics. The model is derived from molecular dynamics by means of a systematic coarse-graining procedure. Thus the…
We propose a method for learning dynamical systems from high-dimensional empirical data that combines variational autoencoders and (spatio-)temporal attention within a framework designed to enforce certain scientifically-motivated…
Throughout the history of science, physics-based modeling has relied on judiciously approximating observed dynamics as a balance between a few dominant processes. However, this traditional approach is mathematically cumbersome and only…
In this paper, we present a general numerical platform for designing accurate, efficient, and stable numerical algorithms for incompressible hydrodynamic models that obeys the thermodynamical laws. The obtained numerical schemes are…
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…
Concepts of everyday use like energy, heat, and temperature have acquired a precise meaning after the development of thermodynamics. Thermodynamics provides the basis for understanding how heat and work are related and with the general…
We introduce a data-driven method for learning the equations of motion of mechanical systems directly from position measurements, without requiring access to velocity data. This is particularly relevant in system identification tasks where…
This work is devoted to the study of dissipative fluid systems, through the lens of a geometric variational formulation. Building upon previous works extending Hamilton's principle to non-equilibrium thermodynamics, the present method…
The dynamics of biological systems, from proteins to cells to organisms, is complex and stochastic. To decipher their physical laws, we need to bridge between experimental observations and theoretical modeling. Thanks to progress in…
We present a general, constructive method to derive thermodynamically consistent models and consistent dynamic boundary conditions hierarchically following the generalized Onsager principle. The method consists of two steps in tandem: the…
Causal discovery is a data-driven paradigm for analyzing complex systems, while physics-based models, such as ordinary differential equations (ODEs), provide mechanistic structure for real-world dynamical processes. Integrating these…
Multiscale systems are ubiquitous in science and technology, but are notoriously challenging to simulate as short spatiotemporal scales must be appropriately linked to emergent bulk physics. When expensive high-dimensional dynamical systems…
The mesoscopic concept is a way to deal with complex materials with an internal structure within continuum mechanics. It consists of extending the domain of the balance equations by mesoscopic variables and of introducing a local…
Experimental data bases are typically very large and high dimensional. To learn from them requires to recognize important features (a pattern), often present at scales different to that of the recorded data. Following the experience…
We present a natural framework for constructing energy-stable time discretization schemes. By leveraging the Onsager principle, we demonstrate its efficacy in formulating partial differential equation models for diverse gradient flow…
The data-driven discovery of long-time macroscopic dynamics and thermodynamics of dissipative systems with particle fidelity is hampered by significant obstacles. These include the strong time-scale limitations inherent to particle…