arXiv subjects

Ben J. Evans

Publications and source records attributed to Ben J. Evans.

5 recordsLinked to original sources

arXiv2025

From Metrics to Meaning: Time to Rethink Evaluation in Human-AI Collaborative Design

As AI systems increasingly shape decision making in creative design contexts, understanding how humans engage with these tools has become a critical challenge for interactive intelligent systems research. This paper contributes a challenge to rethink how to evaluate human--AI collaborative systems, advocating for a more nuanced and multidimensional approach. Findings from one of the largest field studies to date (n = 808) of a human--AI co-creative system, The Genetic Car Designer, complemented by a controlled lab study (n = 12) are presented. The system is based on an interactive evolutionary algorithm where participants were tasked with designing a simple two dimensional representation of a car. Participants were exposed to galleries of design suggestions generated by an intelligent system, MAP--Elites, and a random control. Results indicate that exposure to galleries generated by MAP--Elites significantly enhanced both cognitive and behavioural engagement, leading to higher-quality design outcomes. Crucially for the wider community, the analysis reveals that conventional evaluation methods, which often focus on solely behavioural and design quality metrics, fail to capture the full spectrum of user engagement. By considering the human--AI design process as a changing emotional, behavioural and cognitive state of the designer, we propose evaluating human--AI systems holistically and considering intelligent systems as a core part of the user experience -- not simply a back end tool.

cs.HC↗

arXiv2025

PGD-based local surrogate models via overlapping domain decomposition: a computational comparison

An efficient strategy to construct physics-based local surrogate models for parametric linear elliptic problems is presented. The method relies on proper generalized decomposition (PGD) to reduce the dimensionality of the problem and on an overlapping domain decomposition (DD) strategy to decouple the spatial degrees of freedom. In the offline phase, the local surrogate model is computed in a non-intrusive way, exploiting the linearity of the operator and imposing arbitrary Dirichlet conditions, independently at each node of the interface, by means of the traces of the finite element functions employed for the discretization inside the subdomain. This leads to parametric subproblems with reduced dimensionality, significantly decreasing the complexity of the involved computations and achieving speed-ups up to 100 times with respect to a previously proposed DD-PGD algorithm that required clustering the interface nodes. A fully algebraic alternating Schwarz method is then formulated to couple the subdomains in the online phase, leveraging the real-time (less than half a second) evaluation capabilities of the computed local surrogate models, that do not require the solution of any additional low-dimensional problems. A computational comparison of different PGD-based local surrogate models is presented using a set of numerical benchmarks to showcase the superior performance of the proposed methodology, both in the offline and in the online phase.

math.NA↗

arXiv2025

An overlapping domain decomposition method for parametric Stokes and Stokes-Darcy problems via proper generalized decomposition

A strategy to construct physics-based local surrogate models for parametric Stokes flows and coupled Stokes-Darcy systems is presented. The methodology relies on the proper generalized decomposition (PGD) method to reduce the dimensionality of the parametric flow fields and on an overlapping domain decomposition (DD) paradigm to reduce the number of globally coupled degrees of freedom in space. The DD-PGD approach provides a non-intrusive framework in which end-users only need access to the matrices arising from the (finite element) discretization of the full-order problems in the subdomains. The traces of the finite element functions used for the discretization within the subdomains are employed to impose arbitrary Dirichlet boundary conditions at the interface, without introducing auxiliary basis functions. The methodology is seamless to the choice of the discretization schemes in space, being compatible with both LBB-compliant finite element pairs and stabilized formulations, and the DD-PGD paradigm is transparent to the employed overlapping DD approach. The local surrogate models are glued together in the online phase by solving a parametric interface system to impose continuity of the subdomain solutions at the interfaces, without introducing Lagrange multipliers to enforce the continuity in the entire overlap and without solving any additional physical problem in the reduced space. Numerical results are presented for parametric single-physics (Stokes-Stokes) and multi-physics (Stokes-Darcy) systems, showcasing the accuracy, robustness, and computational efficiency of DD-PGD, and its capability to outperform DD methods based on high-fidelity finite element solvers in terms of computing times.

math.NA↗

arXiv2024

Local surrogate models with reduced dimensionality via overlapping domain decomposition and proper generalized decomposition

We propose an efficient algorithm that combines overlapping domain decomposition and proper generalized decomposition (PGD) to construct surrogate models of linear elliptic parametric problems. The technique is composed of an offline and an online phase that can be implemented in a fully non-intrusive way. The online phase relies on a substructured algebraic formulation of the alternating Schwarz method, while the offline phase exploits the linearity of the boundary value problem to characterize a PGD basis and generate local surrogate models, with minimal parametric dimensionality, in each subdomain. Numerical results show the efficiency of the proposed methodology.

math.NA↗

arXiv2023

An overlapping domain decomposition method for the solution of parametric elliptic problems via proper generalized decomposition

A non-intrusive proper generalized decomposition (PGD) strategy, coupled with an overlapping domain decomposition (DD) method, is proposed to efficiently construct surrogate models of parametric linear elliptic problems. A parametric multi-domain formulation is presented, with local subproblems featuring arbitrary Dirichlet interface conditions represented through the traces of the finite element functions used for spatial discretization at the subdomain level, with no need for additional auxiliary basis functions. The linearity of the operator is exploited to devise low-dimensional problems with only few active boundary parameters. An overlapping Schwarz method is used to glue the local surrogate models, solving a linear system for the nodal values of the parametric solution at the interfaces, without introducing Lagrange multipliers to enforce the continuity in the overlapping region. The proposed DD-PGD methodology relies on a fully algebraic formulation allowing for real-time computation based on the efficient interpolation of the local surrogate models in the parametric space, with no additional problems to be solved during the execution of the Schwarz algorithm. Numerical results for parametric diffusion and convection-diffusion problems are presented to showcase the accuracy of the DD-PGD approach, its robustness in different regimes and its superior performance with respect to standard high-fidelity DD methods.

math.NA↗