When the Model Won’t Invert: Interactive
Visual Optimization of Complex Simulations
K. Matković${}^a$, R. Splechtna${}^a$ and H. Hauser${}^b$
${}^a$VRVis Research Center, Vienna, Austria, ${}^b$University of Bergen, Norway
Many systems in science and engineering can be modeled and simulated, but not solved analytically. The model maps control parameters, etc., to model outputs through coupled, computationally expensive, non-linear equations. Such models are ‘black boxes’: they can be ‘run’ forward, but not inverted. For a desired output, there is no closed-form way to recover the parameters that produced it. This is true wherever the governing physics resist linearization and outputs are shaped by interactions that cannot be decomposed into independent, simple parts. The challenge is not merely computational. Optimization faces three compounding difficulties: the parameter space is usually high-dimensional, making dense sampling prohibitive; objectives are often conflicting, requiring trade-offs that may be user-dependent; and many critical constraints are implicit – an experienced practitioner recognizes them immediately, but they resist formal specification. We present and discuss a methodology integrating simulation, surrogate modeling, and interactive visualization: an initial ensemble of simulation runs sparsely covers the parameter space, a comparably simple surrogate model is fitted to this ensemble, enabling rapid estimation and the swift generation of new candidate solutions. These candidates are presented to the expert user through interactive, domain-familiar visualizations. The expert then explores and refines; new runs are targeted at the region of interest and the cycle continues. Every surviving candidate is checked by means of the fully-fletched simulation. This human-in-the-loop approach is necessary as implicit knowledge cannot be encoded in an objective function, but it can be exercised through a visual interface. We illustrate the approach on two use cases [1, 2], where the workflow reduced design exploration time by at least an order of magnitude.
Keywords: Visualization, surrogate modeling, interactive optimization.