Controlling Soft Matter Instabilities Using Artificial Intelligence

Abstract

Lakshmi N. Sridhar

This work develops a unified framework for modeling, analyzing, and controlling oscillatory instabilities in soft matter systems governed by the Navier–Stokes equations coupled with viscoelastic constitutive laws. A reduced-order model is derived using Galerkin projection, capturing the essential interaction between velocity modes and stress dynamics. Near critical conditions, the system exhibits a Hopf bifurcation, leading to a transition from steady behavior to sustained oscillations. This bifurcation is characterized using continuation analysis, confirming the presence of a limit cycle and highlighting the role of flow–stress coupling in driving instability. To regulate these dynamics, an optimal control formulation is introduced in which the bifurcation parameter is treated as a time-dependent control variable. A key contribution of this work is the incorporation of a smooth, data-driven surrogate model to approximate system stability, enabling stability-aware optimization without explicit eigenvalue computation. The resulting control strategy effectively steers the system away from unstable regimes while maintaining performance, demonstrating a balance between stability enforcement and control effort. The proposed approach integrates reduced-order modeling, bifurcation theory, and machine learning into a computationally tractable framework. This methodology provides a promising tool for managing complex nonlinear behavior in soft matter flows and has potential applications in chemical engineering, materials processing, and fluid dynamics.

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