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Gaussian Graphical Models (GGMs) or Gauss Markov random fields are widely used in many applications, and the trade-off between the modeling capacity and the efficiency of learning and inference has been an important research problem. In…

We propose a novel method to optimize the structure of factor graphs for graph-based inference. As an example inference task, we consider symbol detection on linear inter-symbol interference channels. The factor graph framework has the…

Numerous formalisms and dedicated algorithms have been designed in the last decades to model and solve decision making problems. Some formalisms, such as constraint networks, can express "simple" decision problems, while others are designed…

Deep generative models (DGMs) are effective on learning multilayered representations of complex data and performing inference of input data by exploring the generative ability. However, little work has been done on examining or empowering…

We study optimization algorithms for the finite sum problems frequently arising in machine learning applications. First, we propose novel variants of stochastic gradient descent with a variance reduction property that enables linear…

Deep learning (DL) models require extensive data to achieve strong performance and generalization. Deep generative models (DGMs) offer a solution by synthesizing data. Yet current approaches for tabular data often fail to preserve feature…

The present study proposes a data-driven framework trained with high-fidelity simulation results to facilitate decision making for combustor designs. At its core is a surrogate model employing a machine-learning technique called kriging,…

Solving and optimising Partial Differential Equations (PDEs) in geometrically parameterised domains often requires iterative methods, leading to high computational and time complexities. One potential solution is to learn a direct mapping…

Memory units have been widely used to enrich the capabilities of deep networks on capturing long-term dependencies in reasoning and prediction tasks, but little investigation exists on deep generative models (DGMs) which are good at…

Typical topology optimization methods require complex iterative calculations, which cannot meet the requirements of fast computing applications. The neural network is studied to reduce the time of computing the optimization result, however,…

Generative AI has redefined artificial intelligence, enabling the creation of innovative content and customized solutions that drive business practices into a new era of efficiency and creativity. In this paper, we focus on diffusion…

Minimisation of discrete energies defined over factors is an important problem in computer vision, and a vast number of MAP inference algorithms have been proposed. Different inference algorithms perform better on factor graph models (GMs)…

Machine learning and optimization algorithms have been widely applied in the design and optimization for photonic devices. In this article, we briefly review recent progress of this field of research and show some data-driven applications…

Expensive multi-objective optimization is a prevalent and crucial concern in many real-world scenarios, where sample-efficiency is vital due to the limited evaluations to recover the true Pareto front for decision making. Existing works…

The structural design of functional molecules, also called molecular optimization, is an essential chemical science and engineering task with important applications, such as drug discovery. Deep generative models and combinatorial…

In this article, we present an extension of the formulation recently developed by the authors (A Framework for Data-Driven Computational Mechanics Based on Nonlinear Optimization, arXiv:1910.12736 [math.NA]) to the structural dynamics…

In this work we consider data-driven optimization problems where one must maximize a function given only queries at a fixed set of points. This problem setting emerges in many domains where function evaluation is a complex and expensive…

The local optima network model has proved useful in the past in connection with combinatorial optimization problems. Here we examine its extension to the real continuous function domain. Through a sampling process, the model builds a…

Deep Generative Models (DGMs) have been shown to be powerful tools for generating tabular data, as they have been increasingly able to capture the complex distributions that characterize them. However, to generate realistic synthetic data,…

We consider the problem of optimizing combinatorial spaces (e.g., sequences, trees, and graphs) using expensive black-box function evaluations. For example, optimizing molecules for drug design using physical lab experiments. Bayesian…