Workshop to Assess the Surprising Observed Ease of Optimization of Diverse Control Phenomena Across the Sciences
Abstract
Seeking optimal performance is pervasive in the sciences, including in chemistry, material science, quantum dynamics, and directed evolution. Similarly, it is widely accepted that Nature is performing stochastic optimization in evolution driven by the survival of the fittest. Collectively, all of these optimization phenomena span wide temporal and spatial scales. Most strikingly, all scenarios involve searching over a vast space of control variables, yet the literature shows that dramatic search efficiency is commonly exhibited relative to the number of possible control choices. Importantly, this assessment puts aside possibly arduous overhead (e.g., experimental set up time, etc.). The planned two-day Workshop aims to draw together a group of scientists from each of the aforementioned disciplines as well as appropriate mathematicians for a total of 15 participants. An overarching mathematically-based Hypothesis has been put forth to explain the observed startling ease of reaching optimal control performance. The participants in the Workshop will present and discuss their experiences with optimization in each topical area. In this regard, the notion of optimization is commonplace in the sciences, although such efforts expressed in a control framework is unusual; expressing optimization in terms of a control perspective appears central to explaining the evident systematic behavior found across what appear to be diverse fields. A key aim for the Workshop is to weigh the scope of validity of the underlying explanatory control-based Hypothesis, which is expressed as a theorem in each area of the sciences resting on a common set of assumptions. The theorem serves to assess the topology of the relevant control landscape, which is the particular objective as a function of the control. The assumptions rest on satisfaction of (i) controllability, (ii) local surjectivity, and (iii) availability of fully adequate control resources (i.e., the explicit form of the assumptions is scientific domain specific). In all scientific scenarios studied thus far, the associated theorem shows that trap-free control landscapes are expected to exist, thereby permitting ready optimization of the objectives. The Workshop discussions will also include the prospect of there existing alternative Hypotheses that explain the findings. Regardless of whether the current Hypothesis stands or alternatives are suggested, the Workshop will present a plan for future detailed studies to assess the observed empirical ease of experimental optimization and its analog performed by Nature in evolution as well as consider the fundamental and practical significance of the findings. The present working Hypothesis theorem has recently been extended to a broad class of dynamical systems (i.e., with the same common assumptions stated above), suggesting that like favorable optimization behavior may be found for optimal control of phenomena beyond the natural sciences. The Workshop topic inherently requires drawing together a diverse set of scientific and mathematical participants, and this circumstance calls for careful planning and management over the two-day Workshop. The effort will culminate in a final report including recommendations for future studies guided by the Workshop findings.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Mar 17, 2020
- Source ID
- W911NF2010033
Entities
People
- Herschel A. Rabitz
Organizations
- Army Contracting Command
- Princeton University
- United States Army