Related papers: Differentiable physics-enabled closure modeling fo…
Physically-inspired latent force models offer an interpretable alternative to purely data driven tools for inference in dynamical systems. They carry the structure of differential equations and the flexibility of Gaussian processes,…
We consider the use of Deep Learning methods for modeling complex phenomena like those occurring in natural physical processes. With the large amount of data gathered on these phenomena the data intensive paradigm could begin to challenge…
Computational fluid dynamics models based on Reynolds-averaged Navier--Stokes equations with turbulence closures still play important roles in engineering design and analysis. However, the development of turbulence models has been stagnant…
Important classes of active matter systems can be modeled using kinetic theories. However, kinetic theories can be high dimensional and challenging to simulate. Reduced-order representations based on tracking only low-order moments of the…
Upcoming technologies like digital twins, autonomous, and artificial intelligent systems involving safety-critical applications require models which are accurate, interpretable, computationally efficient, and generalizable. Unfortunately,…
Combining physics with machine learning models has advanced the performance of machine learning models in many different applications. In this paper, we evaluate adding a weak physics constraint, i.e., a physics-based empirical…
Modeling the dynamics of flexible objects has become an emerging topic in the community as these objects become more present in many applications, e.g., soft robotics. Due to the properties of flexible materials, the movements of soft…
Identifying self-similarity is key to understanding and modelling a plethora of phenomena in fluid mechanics. Unfortunately, this is not always possible to perform formally in highly complex flows. We propose a methodology to extract the…
We consider the generalised Burgers equation $$ \frac{\partial u}{\partial t} + f'(u)\frac{\partial u}{\partial x} - \nu \frac{\partial^2 u}{\partial x^2}=0,\ t \geq 0,\ x \in S^1, $$ where $f$ is strongly convex and $\nu$ is small and…
This study aims to enhance the generalizability of Reynolds-averaged Navier-Stokes (RANS) turbulence models, which are crucial for engineering applications. Classic RANS turbulence models often struggle to predict separated flows…
Dissipative models for the quasi-static and dynamic response due to slip in an elastic body containing a single slip plane of vanishing thickness are developed. Discrete dislocations with continuously distributed cores can glide on this…
Turbulent flows consist of a wide range of interacting scales. Since the scale range increases as some power of the flow Reynolds number, a faithful simulation of the entire scale range is prohibitively expensive at high Reynolds numbers.…
With the recent wave of digitalization, specifically in the context of safety-critical applications, there has been a growing need for computationally efficient, accurate, generalizable, and trustworthy models. Physics-based models have…
Many geophysical and astrophysical phenomena are driven by turbulent fluid dynamics, containing behaviors separated by tens of orders of magnitude in scale. While direct simulations have made large strides toward understanding geophysical…
A key challenge to nonlocal models is the analytical complexity of deriving them from first principles, and frequently their use is justified a posteriori. In this work we extract nonlocal models from data, circumventing these challenges…
We present our progress on the application of physics informed deep learning to reservoir simulation problems. The model is a neural network that is jointly trained to respect governing physical laws and match boundary conditions. The…
This dissertation discusses the intermitency phenomenon in three models of turbulence, employing analytical and numerical techniques in the analysis of stochastic processes and the probability distributions which they induce. The initial…
Obtaining predictive low-order models is a central challenge in fluid dynamics. Data-driven frameworks have been widely used to obtain low-order models of aerodynamic systems; yet, resulting models tend to yield predictions that grow…
We study decaying turbulence in the 1D Burgers equation (Burgulence) and 3D Navier-Stokes (NS) turbulence. We first investigate the decay in time $t$ of the energy $E(t)$ in Burgulence, for a fractional Brownian initial potential, with…
We explore a connection of the forced Burgers equation with the Schr\"{o}dinger (diffusive) interpolating dynamics in the presence of deterministic external forces. This entails an exploration of the consistency conditions that allow to…