Decentralized digital twins of complex dynamical systems.

In this article, we introduce a decentralized digital twin (DDT) modeling framework and its potential applications in computational science and engineering. The DDT methodology is based on the idea of federated learning, a subfield of machine learning that promotes knowledge exchange without disclosing actual data. Clients can learn an aggregated model cooperatively using this method while maintaining complete client-specific training data.

An efficient quantum partial differential equation solver with chebyshev points.

Differential equations are the foundation of mathematical models representing the universe's physics. Hence, it is significant to solve partial and ordinary differential equations, such as Navier-Stokes, heat transfer, convection-diffusion, and wave equations, to model, calculate and simulate the underlying complex physical processes. However, it is challenging to solve coupled nonlinear high dimensional partial differential equations in classical computers because of the vast amount of required resources and time.

Variational multiscale reinforcement learning for discovering reduced order closure models of nonlinear spatiotemporal transport systems.

A central challenge in the computational modeling and simulation of a multitude of science applications is to achieve robust and accurate closures for their coarse-grained representations due to underlying highly nonlinear multiscale interactions. These closure models are common in many nonlinear spatiotemporal systems to account for losses due to reduced order representations, including many transport phenomena in fluids. Previous data-driven closure modeling efforts have mostly focused on supervised learning approaches using high fidelity simulation data.

Physics guided neural networks for modelling of non-linear dynamics.

The success of the current wave of artificial intelligence can be partly attributed to deep neural networks, which have proven to be very effective in learning complex patterns from large datasets with minimal human intervention. However, it is difficult to train these models on complex dynamical systems from data alone due to their low data efficiency and sensitivity to hyperparameters and initialisation. This work demonstrates that injection of partially known information at an intermediate layer in a DNN can improve model accuracy, reduce model uncertainty, and yield improved convergence during the training.

Risk-based implementation of COLREGs for autonomous surface vehicles using deep reinforcement learning.

Autonomous systems are becoming ubiquitous and gaining momentum within the marine sector. Since the electrification of transport is happening simultaneously, autonomous marine vessels can reduce environmental impact, lower costs, and increase efficiency. Although close monitoring is still required to ensure safety, the ultimate goal is full autonomy.

Multi-fidelity information fusion with concatenated neural networks.

Recently, computational modeling has shifted towards the use of statistical inference, deep learning, and other data-driven modeling frameworks. Although this shift in modeling holds promise in many applications like design optimization and real-time control by lowering the computational burden, training deep learning models needs a huge amount of data. This big data is not always available for scientific problems and leads to poorly generalizable data-driven models.

Deep neural network enabled corrective source term approach to hybrid analysis and modeling.

In this work, we introduce, justify and demonstrate the Corrective Source Term Approach (CoSTA)-a novel approach to Hybrid Analysis and Modeling (HAM). The objective of HAM is to combine physics-based modeling (PBM) and data-driven modeling (DDM) to create generalizable, trustworthy, accurate, computationally efficient and self-evolving models. CoSTA achieves this objective by augmenting the governing equation of a PBM model with a corrective source term generated using a deep neural network.

Deep Reinforcement Learning Controller for 3D Path Following and Collision Avoidance by Autonomous Underwater Vehicles.

Control theory provides engineers with a multitude of tools to design controllers that manipulate the closed-loop behavior and stability of dynamical systems. These methods rely heavily on insights into the mathematical model governing the physical system. However, in complex systems, such as autonomous underwater vehicles performing the dual objective of path following and collision avoidance, decision making becomes nontrivial.

Multifidelity computing for coupling full and reduced order models.

Hybrid physics-machine learning models are increasingly being used in simulations of transport processes. Many complex multiphysics systems relevant to scientific and engineering applications include multiple spatiotemporal scales and comprise a multifidelity problem sharing an interface between various formulations or heterogeneous computational entities. To this end, we present a robust hybrid analysis and modeling approach combining a physics-based full order model (FOM) and a data-driven reduced order model (ROM) to form the building blocks of an integrated approach among mixed fidelity descriptions toward predictive digital twin technologies.

Interface learning of multiphysics and multiscale systems.

Complex natural or engineered systems comprise multiple characteristic scales, multiple spatiotemporal domains, and even multiple physical closure laws. To address such challenges, we introduce an interface learning paradigm and put forth a data-driven closure approach based on memory embedding to provide physically correct boundary conditions at the interface. To enable the interface learning for hyperbolic systems by considering the domain of influence and wave structures into account, we put forth the concept of upwind learning toward a physics-informed domain decomposition.

Forward sensitivity approach for estimating eddy viscosity closures in nonlinear model reduction.

In this paper, we propose a variational approach to estimate eddy viscosity using forward sensitivity method (FSM) for closure modeling in nonlinear reduced order models. FSM is a data assimilation technique that blends model's predictions with noisy observations to correct initial state and/or model parameters. We apply this approach on a projection based reduced order model (ROM) of the one-dimensional viscous Burgers equation with a square wave defining a moving shock, and the two-dimensional vorticity transport equation formulating a decay of Kraichnan turbulence.

Improved singlet oxygen generation and antimicrobial activity of sulphur-doped graphene quantum dots coupled with methylene blue for photodynamic therapy applications.

Due to their many unique properties, graphene quantum dots (GQDs) have attracted much attention and are a promising material with potential applications in many fields. One application of GQDs is as a photodynamic therapy agent that generates singlet oxygen. In this work, GQDs were grown by focusing nanosecond laser pulses into benzene and then were later combined with methylene blue (MB) and used to eradicate the Gram-negative bacteria, Escherichia coli, and Gram-positive bacteria, Micrococcus luteus.

Extreme learning machine for reduced order modeling of turbulent geophysical flows.

We investigate the application of artificial neural networks to stabilize proper orthogonal decomposition-based reduced order models for quasistationary geophysical turbulent flows. An extreme learning machine concept is introduced for computing an eddy-viscosity closure dynamically to incorporate the effects of the truncated modes. We consider a four-gyre wind-driven ocean circulation problem as our prototype setting to assess the performance of the proposed data-driven approach.