This paper presents an innovative approach to tackle Bayesian inverse problems using physics-informed invertible neural networks (PI-INN). Serving as a neural operator model, PI-INN employs an invertible neural network (INN) to elucidate the relationship between the parameter field and the solution function in latent variable spaces. Specifically, the INN decomposes the latent variable of the parameter field into two distinct components: the expansion coefficients that represent the solution to the forward problem, and the noise that captures the inherent uncertainty associated with the inverse problem. Through precise estimation of the forward mapping and preservation of statistical independence between expansion coefficients and latent noise, PI-INN offers an accurate and efficient generative model for resolving Bayesian inverse problems, even in the absence of labeled data. For a given solution function, PI-INN can provide tractable and accurate estimates of the posterior distribution of the underlying parameter field. Moreover, capitalizing on the INN’s characteristics, we propose a novel independent loss function to effectively ensure the independence of the INN’s decomposition results. The efficacy and precision of the proposed PI-INN are demonstrated through a series of numerical experiments.

The distribution of ions near a charged surface is an important quantity in many biological and material processes, and has been therefore investigated intensively. However, few theoretical and simulation approaches have included the influence of concentration-induced variations in the local dielectric permittivity of an underlying electrolyte solution. Such local variations have long been observed and known to affect the properties of ionic solution in the bulk and around the charged surface. We propose a hybrid computational model that combines Monte Carlo simulations with continuum electrostatic modeling to investigate such properties. A key component in our hybrid model is a semianalytical formula for the ion-ion interaction energy in a dielectrically inhomogeneous environment. This formula is obtained by solving for the Green's function Poisson's equation with ionic-concentration-dependent dielectric permittivity using a harmonic interpolation method and spherical harmonic series. We also construct a self-consistent continuum model of electrostatics to describe the effect of ionic-concentration-dependent dielectric permittivity and the resulting self-energy contribution. With extensive numerical simulations, we verify the convergence of our hybrid simulation scheme, show the qualitatively different structures of ionic distribution due to the concentration-induced dielectric variations, and compare our simulation results with the self-consistent continuum model. In particular, we study the differences between weakly and strongly charged surfaces and multivalencies of counterions. Our hybrid simulations conform particularly the depletion of ionic concentrations near a charged surface and also capture the charge inversion. We discuss several issues and possible further improvement of our approach for simulations of large charged systems.

We introduce an improved bond-based peridynamic (BPD) model for simulating brittle fracture in particle reinforced composites based on a micromodulus correction approach. In the peridynamic (PD) constitutive model of particle reinforced composites, three kinds of interactive bond forces are considered, and precise definition of mechanical properties for PD bonds is essential for the fracture analysis in particle reinforced composites. A new micromodulus model of PD bonds for particle reinforced composites is proposed based on the equivalence between the elastic strain energy density of classical continuum mechanics and peridynamic model and the harmonic average approach. The damage of particle reinforced composites is defined locally at the level of pairwise bond, and the critical stretch criterion is described as a function of fracture energy based on the composite failure theory. The algorithm procedure for the improved BPD model based on the finite element/discontinuous Galerkin finite element method is brought forward in detail. Several numerical examples are performed to test the feasibility and effectiveness of the proposed model and algorithm in analysis of elastic deformation, crack nucleation and propagation in particle reinforced composites. Additionally, the impact of distribution, shape and size of particles on the fractures of composite materials are also investigated. Numerical results demonstrate that the improved BPD model can effectively be used to analyze the fracture in particle reinforced composites. Particle reinforced composite, peridynamics bonds, micromodulus correction, fracture, crack growth path. 74R10, 74S05 COPYRIGHT: © Global Science Press

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