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When predicting physical phenomena through simulation, quantification of the total uncertainty due to multiple sources is as crucial as making sure the underlying numerical model is accurate. Possible sources include irreduciblealeatoricuncertainty due to noise in the data,epistemicuncertainty induced by insufficient data or inadequate parameterization andmodel-formuncertainty related to the use of misspecified model equations. In addition, recently proposed approaches provide flexible ways to combine information from data with full or partial satisfaction of equations that typically encode physical principles. Physics-based regularization interacts in non-trivial ways with aleatoric, epistemic and model-form uncertainty and their combination, and a better understanding of this interaction is needed to improve the predictive performance of physics-informed digital twins that operate under real conditions. To better understand this interaction, with a specific focus on biological and physiological models, this study investigates the decomposition of total uncertainty in the estimation of states and parameters of a differential system simulated with MC X-TFC, a new physics-informed approach for uncertainty quantification based on random projections and Monte Carlo sampling. After an introductory comparison between approaches for physics-informed estimation, MC X-TFC is applied to a six-compartment stiff ODE system, the CVSim-6 model, developed in the context of human physiology. The system is first analysed by progressively removing data while estimating an increasing number of parameters, and subsequently by investigating total uncertainty under model-form misspecification of nonlinear resistance in the pulmonary compartment. In particular, we focus on the interaction between the formulation of the discrepancy term and quantification of model-form uncertainty, and show how additional physics can help in the estimation process. The method demonstrates robustness and efficiency in estimating unknown states and parameters, even with limited, sparse and noisy data. It also offers great flexibility in integrating data with physics for improved estimation, even in cases of model misspecification. This article is part of the theme issue ‘Uncertainty quantification for healthcare and biological systems (Part 1)’. 

The molten sand that is a mixture of calcia, magnesia, alumina and silicate, known as CMAS, is characterized by its high viscosity, density and surface tension. The unique properties of CMAS make it a challenging material to deal with in high-temperature applications, requiring innovative solutions and materials to prevent its buildup and damage to critical equipment. Here, we use multiphase many-body dissipative particle dynamics simulations to study the wetting dynamics of highly viscous molten CMAS droplets. The simulations are performed in three dimensions, with varying initial droplet sizes and equilibrium contact angles. We propose a parametric ordinary differential equation (ODE) that captures the spreading radius behaviour of the CMAS droplets. The ODE parameters are then identified based on the physics-informed neural network (PINN) framework. Subsequently, the closed-form dependency of parameter values found by the PINN on the initial radii and contact angles are given using symbolic regression. Finally, we employ Bayesian PINNs (B-PINNs) to assess and quantify the uncertainty associated with the discovered parameters. In brief, this study provides insight into spreading dynamics of CMAS droplets by fusing simple parametric ODE modelling and state-of-the-art machine-learning techniques. 

Electrolyte solutions play an important role in energy storage devices, whose performance relies heavily on the electrokinetic processes at sub-micron scales. Although fluctuations and stochastic features become more critical at small scales, the long-range Coulomb interactions pose a particular challenge for both theoretical analysis and simulation of fluid systems with fluctuating hydrodynamic and electrostatic interactions. Here, we present a theoretical framework based on the Landau–Lifshitz theory to derive closed-form expressions for fluctuation correlations in electrolyte solutions, indicating significantly different decorrelation processes of ionic concentration fluctuations from hydrodynamic fluctuations, which provides insights for understanding transport phenomena of coupled fluctuating hydrodynamics and electrokinetics. Furthermore, we simulate fluctuating electrokinetic systems using both molecular dynamics (MD) with explicit ions and mesoscopic charged dissipative particle dynamics (cDPD) with semi-implicit ions, from which we identify that the spatial probability density functions of local charge density follow a gamma distribution at sub-nanometre scale (i.e. $$0.3\,{\rm nm}$$ ) and converge to a Gaussian distribution above nanometre scales (i.e. $$1.55\,{\rm nm}$$ ), indicating the existence of a lower limit of length scale for mesoscale models using Gaussian fluctuations. The temporal correlation functions of both hydrodynamic and electrokinetic fluctuations are computed from all-atom MD and mesoscale cDPD simulations, showing good agreement with the theoretical predictions based on the linearized fluctuating hydrodynamics theory. 

Physics-informed deep learning helps detect unknown internal structures and defects with limited nondestructive measurements. 

Over the past two decades Biomedical Engineering has emerged as a major discipline that bridges societal needs of human health care with the development of novel technologies. Every medical institution is now equipped at varying degrees of sophistication with the ability to monitor human health in both non-invasive and invasive modes. The multiple scales at which human physiology can be interrogated provide a profound perspective on health and disease. We are at the nexus of creating “avatars” (herein defined as an extension of “digital twins”) of human patho/physiology to serve as paradigms for interrogation and potential intervention. Motivated by the emergence of these new capabilities, the IEEE Engineering in Medicine and Biology Society, the Departments of Biomedical Engineering at Johns Hopkins University and Bioengineering at University of California at San Diego sponsored an interdisciplinary workshop to define the grand challenges that face biomedical engineering and the mechanisms to address these challenges. The Workshop identified five grand challenges with cross-cutting themes and provided a roadmap for new technologies, identified new training needs, and defined the types of interdisciplinary teams needed for addressing these challenges. The themes presented in this paper include: 1) accumedicine through creation of avatars of cells, tissues, organs and whole human; 2) development of smart and responsive devices for human function augmentation; 3) exocortical technologies to understand brain function and treat neuropathologies; 4) the development of approaches to harness the human immune system for health and wellness; and 5) new strategies to engineer genomes and cells.