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We examine a Geometric Deep Learning model as a thermodynamic system treating the weights as non-quantum and non-relativistic particles. We employ the notion of temperature previously defined in [7] and study it in the various layers for…
Fluid dynamics plays a crucial role in various multiphysics applications, including energy systems, electronics cooling, and biomedical engineering. Developing models for complex coupled systems can be challenging and time-consuming. In…
We provide a complete derivation of hydrodynamic equations for nonrelativistic systems based on quantum field theories of spinless Schr\"odeinger fields, assuming that an initial density operator takes a special form of the local Gibbs…
We introduce a machine-learning approach for identifying hidden structural features of open quantum dynamics under restricted experimental access. Unlike most existing data-driven methods which focus on detection or prediction of dynamical…
A constitutive model is developed to predict the viscoelastic response of polyimide resins that are used in high temperature applications. This model is based on a thermodynamic framework that uses the notion that the `natural…
Mathematical modeling of real-world physical systems requires the consistent combination of a multitude of physical laws and phenomenological models. This challenging task can be greatly simplified by hierarchically decomposing systems into…
Classically, the mechanical response of materials is described through constitutive models, often in the form of constrained ordinary differential equations. These models have a very limited number of parameters, yet, they are extremely…
This paper introduces a novel Transitional Dictionary Learning (TDL) framework that can implicitly learn symbolic knowledge, such as visual parts and relations, by reconstructing the input as a combination of parts with implicit relations.…
Mathematical modeling is an essential step, for example, to analyze the transient behavior of a dynamical process and to perform engineering studies such as optimization and control. With the help of first-principles and expert knowledge, a…
Knowledge graph (KG) embedding methods learn geometric representations of entities and relations to predict plausible missing knowledge. These representations are typically assumed to capture rule-like inference patterns. However, our…
Chaotic dynamics, commonly seen in weather systems and fluid turbulence, are characterized by their sensitivity to initial conditions, which makes accurate prediction challenging. Recent approaches have focused on developing data-driven…
In the present paper, we propose the model of {\it structural information learning machines} (SiLeM for short), leading to a mathematical definition of learning by merging the theories of computation and information. Our model shows that…
Learning and reasoning about physical phenomena is still a challenge in robotics development, and computational sciences play a capital role in the search for accurate methods able to provide explanations for past events and rigorous…
Decision-making in complex systems often relies on machine learning models, yet highly accurate models such as XGBoost and neural networks can obscure the reasoning behind their predictions. In operations research applications,…
The Dirichlet Belief Network~(DirBN) has been recently proposed as a promising approach in learning interpretable deep latent representations for objects. In this work, we leverage its interpretable modelling architecture and propose a deep…
We develop a Lie group geometric framework for the motion of fluids with permeable boundaries that extends Arnold's geometric description of fluid in closed domains. Our setting is based on the classical Hamilton principle applied to fluid…
Behaviors of many engineering systems are described by lumped parameter models that encapsulate the spatially distributed nature of the system into networks of lumped elements; the dynamics of such a network is governed by a system of…
Premixed flames exhibit different asymptotic regimes of interaction between heat release and turbulence depending on their respective length scales. At high Karlovitz number, the dilatation caused by heat release does not have any relevant…
Understanding dissipation in open quantum systems is crucial for the development of robust quantum technologies. In this work, we introduce a Transformer-based machine learning framework to infer time-dependent dissipation rates in quantum…
Molecular design requires systematic and broadly applicable methods to extract structure-property relationships. The focus of this study is on learning thermodynamic properties from molecular-liquid simulations. The methodology relies on an…