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In the realm of supervised learning, Bayesian learning has shown robust predictive capabilities under input and parameter perturbations. Inspired by these findings, we demonstrate the robustness properties of Bayesian learning in the…
We consider a coupled system of partial differential equations describing the interactions between a closed free interface and two viscous incompressible fluids. The fluids are assumed to satisfy the incompressible Navier-Stokes equations…
We formulate the problem of material identification as a problem of optimal control in which the deformation of the specimen is the state variable and the unknown material law is the control variable. We assume that the material obeys…
Using linearized elasticity as a convenient mechanical framework, we show that volumetric growth can be formulated as an optimization-driven process in which the growth tensor is determined implicitly by constrained optimization rather than…
This paper studies controllability properties of recurrent neural networks. The new contributions are: (1) an extension of the result in the previous paper "Complete controllability of continuous-time recurrent neural networks" (Sontag and…
Various models of tumor growth are available in the litterature. A first class describes the evolution of the cell number density when considered as a continuous visco-elastic material with growth. A second class, describes the tumor as a…
In this work, we introduce a novel approach to formulating an artificial viscosity for shock capturing in nonlinear hyperbolic systems by utilizing the property that the solutions of hyperbolic conservation laws are not reversible in time…
Living systems are capable of locomotion, reconfiguration, and replication. To perform these tasks, cells spatiotemporally coordinate the interactions of force-generating, "active" molecules that create and manipulate non-equilibrium…
We demonstrate through numerical solutions of the Oldroyd-B model in a two-dimensional Taylor-Couette geometry that the onset of elastic turbulence in a viscoelastic fluid can be controlled by imposed shear-rate modulations. While for slow…
Non-equilibrium systems display memory, a dependence not merely on their present environment but on previously applied fields. Multistable systems such as spin glasses, martensites and granular matter have exponentially many microstates…
We study controllability issues for the 2D Euler and Navier-Stokes (NS) systems under periodic boundary conditions. These systems describe motion of homogeneous ideal or viscous incompressible fluid on a two-dimensional torus…
We consider a fluid-structure interaction system composed by a rigid ball immersed into a viscous incompressible fluid. The motion of the structure satisfies the Newton laws and the fluid equations are the standard Navier-Stokes system. At…
In this article, we study the existence of insensitizing controls for a nonlinear reaction-diffusion equation with dynamic boundary conditions. Here, we have a partially unknown data of the system, and the problem consists in finding…
We propose and analyze a simple model for the evolution of an immersed, inextensible filament which incorporates linear viscoelastic effects of the surrounding fluid. The model is a closed-form system of equations along the curve only which…
Inspired in our work on the controllability for the semilinear with memory \cite{Carrasco-Guevara-Leiva:2017aa, Guevara-Leiva:2016aa, Guevara-Leiva:2017aa}, we present the general cases for the approximate controllability of impulsive…
Inspired by normalizing flows, we analyze the bilinear control of neural transport equations by means of time-dependent velocity fields restricted to fulfill, at any time instance, a simple neural network ansatz. The L^1 approximate…
To simulate a macroscopic system from a simulation cell, a direct summation of the elastic fields produced by periodic images can be used. If the cell contains a non-zero elastic dipole component, the sum is known to be conditionally…
Irreversible transport in time-periodic flows is commonly attributed to vorticity, nonlinear forcing, or symmetry breaking. We show that finite-memory reconstruction of the velocity gradient generates a purely geometric mechanism for…
The nonlinear mechanics of a flexible elastic rod constrained at its edges by a pair of sliding sleeves is analyzed. The planar equilibrium configurations of this variable-length elastica are found to have shape defined only by the…
Motor control is a fundamental process that underlies all voluntary behavioral responses. Several different theories based on different principles (task dynamics, equilibrium-point theory, passive-motion paradigm, active inference, optimal…