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We consider a class of stochastic programming problems where the implicitly decision-dependent random variable follows a nonparametric regression model with heteroscedastic error. The Clarke subdifferential and surrogate functions are not…
We propose a novel \textit{capsule} based deep encoder-decoder model for surrogate modeling and uncertainty quantification of systems in mechanics from sparse data. The proposed framework is developed by adapting Capsule Network (CapsNet)…
Evolutionary Strategies (ES) are known to be an effective black-box optimization technique for deep neural networks when the true gradients cannot be computed, such as in Reinforcement Learning. We continue a recent line of research that…
Well-established methods for the solution of stochastic partial differential equations (SPDEs) typically struggle in problems with high-dimensional inputs/outputs. Such difficulties are only amplified in large-scale applications where even…
This paper proposes a novel deep generative model, called BSDE-Gen, which combines the flexibility of backward stochastic differential equations (BSDEs) with the power of deep neural networks for generating high-dimensional complex target…
Understanding the training dynamics of deep learning models is perhaps a necessary step toward demystifying the effectiveness of these models. In particular, how do data from different classes gradually become separable in their feature…
Supervised deep-embedding methods project inputs of a domain to a representational space in which same-class instances lie near one another and different-class instances lie far apart. We propose a probabilistic method that treats…
This work considers stochastic Galerkin approximations of linear elliptic partial differential equations (PDEs) with stochastic forcing terms and stochastic diffusion coefficients, that cannot be bounded uniformly away from zero and…
Modeling the traffic dynamics is essential for understanding and predicting the traffic spatiotemporal evolution. However, deriving the partial differential equation (PDE) models that capture these dynamics is challenging due to their…
Autoregressive next-step prediction models have become the de-facto standard for building data-driven neural solvers to forecast time-dependent partial differential equations (PDEs). Denoise training that is closely related to diffusion…
The term `surrogate modeling' in computational science and engineering refers to the development of computationally efficient approximations for expensive simulations, such as those arising from numerical solution of partial differential…
Microstructural evolution is a key aspect of understanding and exploiting the structure-property-performance relation of materials. Modeling microstructure evolution usually relies on coarse-grained simulations with evolution principles…
Probabilistic graphical modeling (PGM) provides a framework for formulating an interpretable generative process of data and expressing uncertainty about unknowns, but it lacks flexibility. Deep learning (DL) is an alternative framework for…
Learning in uncertain, noisy, or adversarial environments is a challenging task for deep neural networks (DNNs). We propose a new theoretically grounded and efficient approach for robust learning that builds upon Bayesian estimation and…
Surrogate models for partial-differential equations are widely used in the design of meta-materials to rapidly evaluate the behavior of composable components. However, the training cost of accurate surrogates by machine learning can rapidly…
Ordinary and partial differential equations (ODEs/PDEs) play a paramount role in analyzing and simulating complex dynamic processes across all corners of science and engineering. In recent years machine learning tools are aspiring to…
Uncertainty quantification is a fundamental yet unsolved problem for deep learning. The Bayesian framework provides a principled way of uncertainty estimation but is often not scalable to modern deep neural nets (DNNs) that have a large…
A novel refinement measure for non-intrusive surrogate modelling of partial differential equations (PDEs) with uncertain parameters is proposed. Our approach uses an empirical interpolation procedure, where the proposed refinement measure…
Inspired by the ubiquitous use of differential equations to model continuous dynamics across diverse scientific and engineering domains, we propose a novel and intuitive approach to continuous sequence modeling. Our method interprets…
High-fidelity simulation of complex physical systems is exorbitantly expensive and inaccessible across spatiotemporal scales. Recently, there has been an increasing interest in leveraging deep learning to augment scientific data based on…