A Hierarchical Framework for Inverse Problems in Biological Cybernetics: Opportunities and Limitations

We consider the problem of reconstructing biological mechanisms from experimental data by means of mathematical models. This class of problems is usually known as inverse problems. We argue that this problem admits a natural hierarchy of increasing ambition and complexity: from estimating parameters of a known model, to discovering model structure from data, to inferring the optimality principles that govern system behavior, and finally to characterizing the strategic objectives of multiple competing biological agents. In this study we examine the mathematical foundations, practical utility, and fundamental limitations of each level of this hierarchy. Our discussion draws on arguments from both proponents and critics of the framework. For that, we assess the evidential basis for applying optimality principles to biological systems, contributing to the long-standing debate on this topic. We also discuss the relationship between this hierarchy and analogous problems in modern machine learning and artificial intelligence. Our conclusion is that the lower levels rest on quite mature theoretical and computational foundations, while the upper levels represent a compelling but more speculative research frontier whose biological validity must be established empirically rather than assumed on theoretical grounds. Throughout, we argue that the appropriate standard for optimality-based modeling in biology is not proof of correctness, but rather its potential usefulness: the generation of falsifiable hypotheses, the prediction of experimental outcomes, and the organization of otherwise disconnected observations into coherent mechanistic models.