Related papers: Basis Adaptive Sample Efficient Polynomial Chaos (…
We present a novel approach for solving steady-state stochastic partial differential equations (PDEs) with high-dimensional random parameter space. The proposed approach combines spatial domain decomposition with basis adaptation for each…
The recently introduced basis adaptation method for Homogeneous (Wiener) Chaos expansions is explored in a new context where the rotation/projection matrices are computed by discovering the active subspace where the random input exhibits…
Approximate Bayesian Computation (ABC) methods are commonly used to approximate posterior distributions in models with unknown or computationally intractable likelihoods. Classical ABC methods are based on nearest neighbor type algorithms…
To infer the parameters of mechanistic models with intractable likelihoods, techniques such as approximate Bayesian computation (ABC) are increasingly being adopted. One of the main disadvantages of ABC in practical situations, however, is…
Surrogate modeling of costly mathematical models representing physical systems is challenging since it is typically not possible to create a large experimental design. Thus, it is beneficial to constrain the approximation to adhere to the…
Approximate Bayesian Computation (ABC) is a powerful method for carrying out Bayesian inference when the likelihood is computationally intractable. However, a drawback of ABC is that it is an approximate method that induces a systematic…
Basis adaptation in Homogeneous Chaos spaces rely on a suitable rotation of the underlying Gaussian germ. Several rotations have been proposed in the literature resulting in adaptations with different convergence properties. In this paper…
Presence of a high-dimensional stochastic parameter space with discontinuities poses major computational challenges in analyzing and quantifying the effects of the uncertainties in a physical system. In this paper, we propose a stochastic…
This paper proposes an adaptive sparse polynomial chaos expansion(PCE)-based method to quantify the impacts of uncertainties on critical clearing time (CCT) that is an important index in transient stability analysis. The proposed method can…
This work explores a novel approach for adaptive, differentiable parametrization of large-scale non-stationary random fields. Coupled with any gradient-based algorithm, the method can be applied to variety of optimization problems,…
In complex and unknown processes, global models are initially generated over the entire experimental space but often fail to provide accurate predictions in local areas. A common approach is to use local models, which requires partitioning…
In this paper we propose an algorithm for recovering sparse orthogonal polynomials using stochastic collocation. Our approach is motivated by the desire to use generalized polynomial chaos expansions (PCE) to quantify uncertainty in models…
Polynomial Chaos Expansions (PCEs) are widely recognized for their efficient computational performance in surrogate modeling. Yet, a robust framework to quantify local model errors is still lacking. While the local uncertainty of PCE…
The non-intrusive generalized Polynomial Chaos (gPC) method is a popular computational approach for solving partial differential equations (PDEs) with random inputs. The main hurdle preventing its efficient direct application for…
In this paper, we introduce a multiscale framework based on adaptive edge basis functions to solve second-order linear elliptic PDEs with rough coefficients. One of the main results is that we prove the proposed multiscale method achieves…
This work introduces a formulation of model predictive control (MPC) which adaptively reasons about the complexity of the model based on the task while maintaining feasibility and stability guarantees. Existing MPC implementations often…
Model Predictive Control (MPC) is a method to control nonlinear systems with guaranteed stability and constraint satisfaction but suffers from high computation times. Approximate MPC (AMPC) with neural networks (NNs) has emerged to address…
We here adapt an extended version of the adaptive cubic regularisation method with dynamic inexact Hessian information for nonconvex optimisation in [3] to the stochastic optimisation setting. While exact function evaluations are still…
This paper presents a stochastic model predictive control approach for nonlinear systems subject to time-invariant probabilistic uncertainties in model parameters and initial conditions. The stochastic optimal control problem entails a cost…
This paper presents a method for performing Uncertainty Quantification in high-dimensional uncertain spaces by combining arbitrary polynomial chaos with a recently proposed scheme for sensitivity enhancement (1). Including available…