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Direct Preference Optimisation (DPO) has emerged as a powerful method for aligning Large Language Models (LLMs) with human preferences, offering a stable and efficient alternative to approaches that use Reinforcement learning via Human…

Recent advancements in Direct Preference Optimization (DPO) have significantly enhanced the alignment of Large Language Models (LLMs) with human preferences, owing to its simplicity and effectiveness. However, existing methods typically…

In high-dimensional settings, Bayesian optimization (BO) can be expensive and infeasible. The random embedding Bayesian optimization algorithm is commonly used to address high-dimensional BO challenges. However, this method relies on the…

Robust topology optimization (RTO) improves the robustness of designs with respect to random sources in real-world structures, yet an accurate sensitivity analysis requires the solution of many systems of equations at each optimization…

In this experience report, we apply deep active learning to the field of design optimization to reduce the number of computationally expensive numerical simulations. We are interested in optimizing the design of structural components, where…

In this paper, we propose a Dimension-Reduced Second-Order Method (DRSOM) for convex and nonconvex (unconstrained) optimization. Under a trust-region-like framework, our method preserves the convergence of the second-order method while…

This work presents DCFlow, a novel unsupervised cross-modal flow estimation framework that integrates a decoupled optimization strategy and a cross-modal consistency constraint. Unlike previous approaches that implicitly learn flow…

Dynamic mode decomposition (DMD) is an efficient tool for decomposing spatio-temporal data into a set of low-dimensional modes, yielding the oscillation frequencies and the growth rates of physically significant modes. In this paper, we…

Bayesian Optimization (BO) is a method for globally optimizing black-box functions. While BO has been successfully applied to many scenarios, developing effective BO algorithms that scale to functions with high-dimensional domains is still…

Several fundamental problems in science and engineering consist of global optimization tasks involving unknown high-dimensional (black-box) functions that map a set of controllable variables to the outcomes of an expensive experiment.…

Differentiable planning enables gradient-based optimization of decision-making problems by leveraging differentiable models of system dynamics. However, in highly nonlinear and hybrid discrete-continuous domains, the resulting optimization…

The dynamic mode decomposition (DMD) has become a leading tool for data-driven modeling of dynamical systems, providing a regression framework for fitting linear dynamical models to time-series measurement data. We present a simple…

Gradient-based methods are well-suited for derivative-free optimization (DFO), where finite-difference (FD) estimates are commonly used as gradient surrogates. Traditional stochastic approximation methods, such as Kiefer-Wolfowitz (KW) and…

We introduce MoTIF, a mode-structured tensor framework for multi-parametric approximation, super-resolution, and temporal forecasting of high-dimensional unsteady systems. The methodology leverages High-Order Singular Value Decomposition…

This paper presents a new implementation of deterministic multiobjective (MO) optimization called Multiobjective Fractal Decomposition Algorithm (Mo-FDA). The original algorithm was designed for mono-objective large scale continuous…

In the presence of strong heterogeneities, it is well known that the use of explicit schemes for the transport of species in a porous medium suffers from severe restrictions on the time step. This has led to the development of implicit…

We present a new methodology for the real-time reduced-order modeling of stochastic partial differential equations called the dynamically/bi-orthonormal (DBO) decomposition. In this method, the stochastic fields are approximated by a…

In this paper (part 1), we describe a derivative-free trust-region method for solving unconstrained optimization problems. We will discuss a method when we relax the model order assumption and use artificial neural network techniques to…

We introduce a novel framework for decentralized projection-free optimization, extending projection-free methods to a broader class of upper-linearizable functions. Our approach leverages decentralized optimization techniques with the…

Methodologies for reducing the design-space dimensionality in shape optimization have been recently developed based on unsupervised machine learning methods. These methods provide reduced dimensionality representations of the design space,…