A Data-Driven Approach to Morphogenesis under Structural Instability

TL;DR

A machine-learning framework is proposed based on the physical modeling of morphogenesis triggered by internal or external forcing to understand and predict their spatiotemporal complexities.

Abstract

Morphological development into evolutionary patterns under structural instability is ubiquitous in living systems and often of vital importance for engineering structures. Here we propose a data-driven approach to understand and predict their spatiotemporal complexities. A machine-learning framework is proposed based on the physical modeling of morphogenesis triggered by internal or external forcing. Digital libraries of structural patterns are constructed from the simulation data, which are then used to recognize the abnormalities, predict their development, and assist in risk assessment and prognosis. The capabilities to identify the key bifurcation characteristics and predict the history-dependent development from the global and local features are demonstrated by examples of brain growth and aerospace structural design, which offer guidelines for disease diagnosis/prognosis and instability-tolerant design.

Figures (4)

• Figure 1: The machine-learning framework for pattern development.a, Morphogenesis, digital models, and pattern development. b, Disease diagnosis and instability-tolerant design in the brain growth and aerospace structural design. c, The neural-network framework to address the spatiotemporal complexities of morphogenesis.
• Figure 2: Identification and prediction of morphological development.a-c, Sequences of structural features involving global feature gyrification index (GI) ( a), local feature localization factor ($L_{\rm F}$) ( b), and the absolute values of dynamical eigenvalues (DEVs) ( c). d, Unsupervised clustering of morphologies in the space spanned by GI and curvature. e, The confusion matrix of recognized brain morphologies. f, The representative morphological samples and corresponding probabilities predicted by the models, in which a high probability value indicates the ability of models to identify the morphology of the simulated brain. g, Predicted map of brain growth. h, The Chamfer distance calculated between predicted final morphology and the ground truth as $t_{\rm obs}$ increases. i, The branching behaviors can be accurately characterized during brain growth.
• Figure 3: Instability-tolerant design for aerospace structures.a, Real-time predictions of pattern evolution for aerospace structures. b, Instability-tolerant design enlarges the permissible regions in design in comparison with traditional design.
• Figure 4: Bifurcation behaviors and rare events.a, The bifurcation nature of pattern development for brain growth and aerospace structural design is identified as fold bifurcation by the analysis of DEVs. b, Rare events generate complex morphological patterns and structural failures. c, The bifurcation diagram covered by the constructed digital libraries can be fully explored, in stark contrast with the single-path nature in path-following methods keller1987path-following.