Related papers: A variance reduction strategy for numerical random…
We present a hybrid sampling-surrogate approach for reducing the computational expense of uncertainty quantification in nonlinear dynamical systems. Our motivation is to enable rapid uncertainty quantification in complex mechanical systems…
Variational inference is a powerful paradigm for approximate Bayesian inference with a number of appealing properties, including support for model learning and data subsampling. By contrast MCMC methods like Hamiltonian Monte Carlo do not…
In this paper, we study numerical methods for the homogenization of linear second-order elliptic equations in nondivergence-form with periodic diffusion coefficients and large drift terms. Upon noting that the effective diffusion matrix can…
In this paper, we analyze the embedding cell method, an algorithm which has been developed for the numerical homogenization of metal-ceramic composite materials. We show the convergence of the iteration scheme of this algorithm and the…
A minimal requirement for simulating multi-scale systems is to reproduce the statistical behavior of the slow variables. In particular, a good numerical method should accurately aproximate the probability density function of the…
Fully resolving dynamics of materials with rapidly-varying features involves expensive fine-scale computations which need to be conducted on macroscopic scales. The theory of homogenization provides an approach to derive effective…
Heterogeneous porous materials play a crucial role in various engineering systems. Microstructure characterization and reconstruction provide effective means for modeling these materials, which are critical for conducting physical property…
This paper presents an efficient variational inference framework for deriving a family of structured gaussian process regression network (SGPRN) models. The key idea is to incorporate auxiliary inducing variables in latent functions and…
We consider a general nonlinear regression problem where the predictors contain measurement error. It has been recently discovered that several well-known dimension reduction methods, such as OLS, SIR and pHd, can be performed on the…
Penalized empirical risk minimization with a surrogate loss function is often used to learn a high-dimensional linear decision rule in classification problems. Although much of the literature focus on the generalization error, there is a…
This article is concerned with numerical methods to approximate effective coefficients in stochastic homogenization of discrete linear elliptic equations, and their numerical analysis --- which has been made possible by recent contributions…
We present a computational framework for two-scale asymptotic homogenization to determine the intrinsic magnetic permeability of composites. To this end, considering linear magnetostatics, both vector and scalar potential formulations are…
In representation learning, uniformity refers to the uniform feature distribution in the latent space (i.e., unit hypersphere). Previous work has shown that improving uniformity contributes to the learning of under-represented classes.…
A surrogate-based topology optimisation algorithm for linear elastic structures under parametric loads and boundary conditions is proposed. Instead of learning the parametric solution of the state (and adjoint) problems or the optimisation…
Multidisciplinary design optimization methods aim at adapting numerical optimization techniques to the design of engineering systems involving multiple disciplines. In this context, a large number of mixed continuous, integer and…
Elastomeric mechanical metamaterials exhibit unconventional behaviour, emerging from their microstructures often deforming in a highly nonlinear and unstable manner. Such microstructural pattern transformations lead to non-local behaviour…
In this paper, we apply shrinkage strategies to estimate regression coefficients efficiently for the high-dimensional multiple regression model, where the number of samples is smaller than the number of predictors. We assume in the sparse…
Fast inference of numerical model parameters from data is an important prerequisite to generate predictive models for a wide range of applications. Use of sampling-based approaches such as Markov chain Monte Carlo may become intractable…
Deep learning has proven to be effective in a wide variety of loss minimization problems. However, many applications of interest, like minimizing projected Bellman error and min-max optimization, cannot be modelled as minimizing a scalar…
This paper proposes an embedding method for co-occurrence data aimed at visual information exploration. We consider cases where co-occurrence probabilities are measured between pairs of elements from heterogeneous domains. The proposed…