Complex System Exploration with Interactive Human Guidance

TL;DR

This paper tackles the challenge of exploring complex, high-dimensional systems by enabling interactive, ROI-guided exploration that maximizes constrained diversity while preserving global diversity. It introduces a constrained-diversity variant of Intrinsically Motivated Goal Exploration Process (IMGEP) with an augmented history and a balanced sampling policy that biases search toward user-defined regions of interest (ROI) expressed as explicit constraints. Empirical results on Gray-Scott and Lenia show that the NRAB method substantially improves ROI acceptance and constrained diversity without sacrificing global diversity, demonstrating the practicality of human-in-the-loop guidance for sample-efficient discovery. The approach is system-agnostic, adapts ROI on the fly, and lays groundwork for broader applications in science and generative arts where user expectations shape pattern discovery.

Abstract

The diversity of patterns that emerge from complex systems motivates their use for scientific or artistic purposes. When exploring these systems, the challenges faced are the size of the parameter space and the strongly non-linear mapping between parameters and emerging patterns. In addition, artists and scientists who explore complex systems do so with an expectation of particular patterns. Taking these expectations into account adds a new set of challenges, which the exploration process must address. We provide design choices and their implementation to address these challenges; enabling the maximization of the diversity of patterns discovered in the user's region of interest -- which we call the constrained diversity -- in a sample-efficient manner. The region of interest is expressed in the form of explicit constraints. These constraints are formulated by the user in a system-agnostic way, and their addition enables interactive system exploration leading to constrained diversity, while maintaining global diversity.

Figures (4)

• Figure 1: Our method explores the parameter space of complex systems to discover patterns that belong to the user's region of interest. Compared to global diversity search, our constrained diversity search approach allows the exploration process to be guided toward user-specific patterns. In this example, the user expects to obtain images with a dark area proportion belonging to $[0.3, 0.4]$.
• Figure 2: Overview of our approach. Our goal is to define a procedure for exploring the parameter space $\Theta$ of a complex system, taking into account the target user's ROI (closed region) in a behavior space $\mathcal{B}$. A random sampling in $\Theta$ leads to a poor diversity in $\mathcal{B}$. Diversity-based methods usually achieve a high global diversity. However, most of the samples end up outside the ROI. Our goal is to find a sampling method that maximizes constrained diversity (i.e., resulting in more samples inside the user's ROI and whose diversity is maximized). To this end, we introduce an IMGEP variant that relies on an additional constraint space $\mathcal{C}$ in which the ROI is more easily expressible than in $\mathcal{B}$.
• Figure 3: Diversity measured during exploration of Gray Scott reaction-diffusion and Lenia. Per each configuration, a total of $50$ run as been conducted with different random seed, the mean is depicted by curves, shaded areas represent std. The representation space used to measure diversity corresponds to the 13 Haralick features haralick_textural_1973 extracted from the observation, standardized and projected in a 4 dimensional space by a principal component analysis. The $N_{init} = 250$ first samples are chosen randomly. (a) Global diversity of Gray-Scott using $N_{bin} := 200,000$. (b) Constrained diversity of Gray-Scott using $N_{bin} := 100,000$. (c) Global diversity of Lenia using $N_{bin} := 200,000$. (d) Constrained diversity of Lenia using $N_{bin} := 100,000$. We use the following parameters. For (a,b): $f \in [0.001, 0.2]$, $\sigma_m(f)=0.2$; $k \in [0.01, 0.075]$, $\sigma_m(k)=0.001$. For (c,d): $R \in [2, 40]$; $T = \frac{1}{dt} \in [2, 20]$; $\mu_k \in [0.05, 0.5]$; $\sigma_k \in [0.001, 0.18]$; $h_k \in [0.01, 1]$; $r_k \in [0.2, 1]$; $b_i \in [0.001, 1]$; $w_i \in [0.01, 0.5]$; $a_i \in [0, 1]$. All $\sigma_m$ are equal to $0.2$, except $\sigma_m(T)=0.5$ and $\sigma_m(\sigma_k)=0.01$.
• Figure 4: Study of the balancing meta-parameter. The conditions are similar to those described in the Section \ref{['sec:results']}. Each point represents the diversity after $1000$ samples using NRAB method, divided by the maximum diversity encountered, for (a) Gray-Scott and (b) Lenia.