Related papers: Stochastic spectral embedding
Fatigue crack growth is one of the most common types of deterioration in metal structures with significant implications on their reliability. Recent advances in Structural Health Monitoring (SHM) have motivated the use of structural…
This study addresses the inverse problem of parameter estimation for Stochastic Differential Equations (SDEs) by minimizing a regularized discrepancy functional via Stochastic Gradient Descent (SGD). To achieve computational efficiency, we…
We develop the method of stochastic modified equations (SME), in which stochastic gradient algorithms are approximated in the weak sense by continuous-time stochastic differential equations. We exploit the continuous formulation together…
I propose a novel framework that integrates stochastic differential equations (SDEs) with deep generative models to improve uncertainty quantification in machine learning applications involving structured and temporal data. This approach,…
Sparse regression on a library of candidate features has developed as the prime method to discover the partial differential equation underlying a spatio-temporal data-set. These features consist of higher order derivatives, limiting model…
Variational autoencoders (VAEs) are a popular class of deep generative models with many variants and a wide range of applications. Improvements upon the standard VAE mostly focus on the modelling of the posterior distribution over the…
The self-consistent expansion (SCE) is a powerful technique for obtaining perturbative solutions to problems in statistical physics but it suffers from a subtle problem - too much freedom! The SCE can be used to generate an enormous number…
Data-driven surrogate models are widely used for applications such as design optimization and uncertainty quantification, where repeated evaluations of an expensive simulator are required. For most partial differential equation (PDE)…
Sparse reduced-rank regression is an important tool to uncover meaningful dependence structure between large numbers of predictors and responses in many big data applications such as genome-wide association studies and social media…
Dynamic relational data arise in many machine learning applications, yet their evolving structure poses challenges for learning representations that remain consistent and interpretable over time. A common approach is to learn time varying…
We propose a statistical-stochastic surrogate modeling approach to predict the response of the mean and variance statistics under various initial conditions and external forcing perturbations. The proposed modeling framework extends the…
We target time-dependent partial differential equations (PDEs) with heterogeneous coefficients in space and time. To tackle these problems, we construct reduced basis/ multiscale ansatz functions defined in space that can be combined with…
Parametric embedding methods such as parametric t-SNE (pt-SNE) have been widely adopted for data visualization and out-of-sample data embedding without further computationally expensive optimization or approximation. However, the…
Developing efficient numerical algorithms for the solution of high dimensional random Partial Differential Equations (PDEs) has been a challenging task due to the well-known curse of dimensionality. We present a new solution framework for…
High-dimensional complex multi-parameter problems are prevalent in engineering, exceeding the capabilities of traditional surrogate models designed for low/medium-dimensional problems. These models face the curse of dimensionality,…
Stochastic Neighbor Embedding (SNE) methods minimize the divergence between the similarity matrix of a high-dimensional data set and its counterpart from a low-dimensional embedding, leading to widely applied tools for data visualization.…
Stochastic Petri Nets (SPNs) are an increasingly popular tool of choice for modeling discrete-event dynamics in areas such as epidemiology and systems biology, yet their parameter estimation remains challenging in general and in particular…
We formalize and study the natural approach of designing convex surrogate loss functions via embeddings, for problems such as classification, ranking, or structured prediction. In this approach, one embeds each of the finitely many…
The Stochastic Series Expansion method (SSE) is a Quantum Monte Carlo (QMC) technique working directly in the imaginary time continuum and thus avoiding "Trotter discretization" errors. Using a non-local "operator-loop update" it allows…
We propose a deep learning-based surrogate model for stochastic simulators. The basic idea is to use generative neural network to approximate the stochastic response. The challenge with such a framework resides in designing the network…