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Machine learning (ML) and artificial intelligence (AI) have the remarkable ability to classify, recognize, and characterize complex patterns and trends in large data sets. Here, we adopt a subclass of machine learning methods viz., deep…
As it stands, a robust mathematical framework to analyse and study various topics in deep learning is yet to come to the fore. Nonetheless, viewing deep learning as a dynamical system allows the use of established theories to investigate…
Deep learning has shown great potential for modeling the physical dynamics of complex particle systems such as fluids. Existing approaches, however, require the supervision of consecutive particle properties, including positions and…
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…
Simulating fluid flow around arbitrary shapes is key to solving various engineering problems. However, simulating flow physics across complex geometries remains numerically challenging and computationally resource-intensive, particularly…
Is a deep learning model capable of understanding systems governed by certain first principle laws by only observing the system's output? Can deep learning learn the underlying physics and honor the physics when making predictions? The…
Weather forecasting is essential but remains computationally intensive and physically incomplete in traditional numerical weather prediction (NWP) methods. Deep learning (DL) models offer efficiency and accuracy but often ignore physical…
Knowledge of the underlying mechanisms of multiphase flow dynamics in porous media is crucial for optimizing subsurface engineering applications like geological carbon sequestration. However, studying the micro-mechanisms of multiphase…
The non-equilibrium high-speed compressible flows present wealthy applications in engineering and science. With the deepening of Thermodynamic Non-Equilibrium (TNE), higher-order non-conserved kinetic moments of the distribution function…
In this work the issue of whether key energetic properties (nonlinear, exponential-type dissipation in the abscence of forcing and long-term stability under conditions of time dependent loading) are automatically inherited by deforming…
To fully understand, analyze, and determine the behavior of dynamical systems, it is crucial to identify their intrinsic modal coordinates. In nonlinear dynamical systems, this task is challenging as the modal transformation based on the…
In this paper, we present a physics-based deep learning framework for data-driven prediction of wave propagation in fluid media. The proposed approach, termed Multistep Integration-Inspired Attention (MI2A), combines a denoising-based…
In the process of the deep learning, we integrate more integrable information of nonlinear wave models, such as the conservation law obtained from the integrable theory, into the neural network structure, and propose a conservation-law…
Modeling nonlinear spatiotemporal dynamical systems has primarily relied on partial differential equations (PDEs). However, the explicit formulation of PDEs for many underexplored processes, such as climate systems, biochemical reaction and…
Continuum-scale material deformation models, such as crystal plasticity, can significantly enhance their predictive accuracy by incorporating input from lower-scale (i.e., mesoscale) models. The procedure to generate and extract the…
The DeeP-Mod framework builds an environment model using features from a Deep Dynamic Programming Network (DDPN), trained via a Deep Q-Network (DQN). While Deep Q-Learning is effective in decision-making, state information is lost in deeper…
(abridged) We present a detailed derivation of a simple hydrodynamic two-fluid model, which aims at the description of the phase separation of non-entangled polymer solutions, where viscoelastic effects play a role. It is directly based…
A slowly-varying or thin-layer multiscale assumption empowers macroscale understanding of many physical scenarios from dispersion in pipes and rivers, including beams, shells, and the modulation of nonlinear waves, to homogenisation of…
In this paper we study the deformations of bihamiltonian PDEs of hydrodynamic type with one dependent variable. The reason we study such deformations is that the deformed systems maintain an infinite number of commuting integrals of motion…
Traditional data-driven deep learning models often struggle with high training costs, error accumulation, and poor generalizability in complex physical processes. Physics-informed deep learning (PiDL) addresses these challenges by…