A Physics-informed Deep Learning Approach for Minimum Effort Stochastic
Control of Colloidal Self-Assembly
- URL: http://arxiv.org/abs/2208.09182v1
- Date: Fri, 19 Aug 2022 07:01:57 GMT
- Title: A Physics-informed Deep Learning Approach for Minimum Effort Stochastic
Control of Colloidal Self-Assembly
- Authors: Iman Nodozi, Jared O'Leary, Ali Mesbah, Abhishek Halder
- Abstract summary: The control objective is formulated in terms of steering the state PDFs from a prescribed initial probability measure towards a prescribed terminal probability measure with minimum control effort.
We derive the conditions of optimality for the associated optimal control problem.
The performance of the proposed solution is demonstrated via numerical simulations on a benchmark colloidal self-assembly problem.
- Score: 9.791617215182598
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: We propose formulating the finite-horizon stochastic optimal control problem
for colloidal self-assembly in the space of probability density functions
(PDFs) of the underlying state variables (namely, order parameters). The
control objective is formulated in terms of steering the state PDFs from a
prescribed initial probability measure towards a prescribed terminal
probability measure with minimum control effort. For specificity, we use a
univariate stochastic state model from the literature. Both the analysis and
the computational steps for control synthesis as developed in this paper
generalize for multivariate stochastic state dynamics given by generic
nonlinear in state and non-affine in control models. We derive the conditions
of optimality for the associated optimal control problem. This derivation
yields a system of three coupled partial differential equations together with
the boundary conditions at the initial and terminal times. The resulting system
is a generalized instance of the so-called Schr\"{o}dinger bridge problem. We
then determine the optimal control policy by training a physics-informed deep
neural network, where the "physics" are the derived conditions of optimality.
The performance of the proposed solution is demonstrated via numerical
simulations on a benchmark colloidal self-assembly problem.
Related papers
- Harmonic Path Integral Diffusion [0.4527270266697462]
We present a novel approach for sampling from a continuous multivariate probability distribution.
Our method constructs a time-dependent bridge from a delta function centered at the origin of the state space.
arXiv Detail & Related papers (2024-09-23T16:20:21Z) - Optimal control for state preparation in two-qubit open quantum systems
driven by coherent and incoherent controls via GRAPE approach [77.34726150561087]
We consider a model of two qubits driven by coherent and incoherent time-dependent controls.
The dynamics of the system is governed by a Gorini-Kossakowski-Sudarshan-Lindblad master equation.
We study evolution of the von Neumann entropy, purity, and one-qubit reduced density matrices under optimized controls.
arXiv Detail & Related papers (2022-11-04T15:20:18Z) - Neural ODEs as Feedback Policies for Nonlinear Optimal Control [1.8514606155611764]
We use Neural ordinary differential equations (Neural ODEs) to model continuous time dynamics as differential equations parametrized with neural networks.
We propose the use of a neural control policy posed as a Neural ODE to solve general nonlinear optimal control problems.
arXiv Detail & Related papers (2022-10-20T13:19:26Z) - On optimization of coherent and incoherent controls for two-level
quantum systems [77.34726150561087]
This article considers some control problems for closed and open two-level quantum systems.
The closed system's dynamics is governed by the Schr"odinger equation with coherent control.
The open system's dynamics is governed by the Gorini-Kossakowski-Sudarshan-Lindblad master equation.
arXiv Detail & Related papers (2022-05-05T09:08:03Z) - Deep Learning Approximation of Diffeomorphisms via Linear-Control
Systems [91.3755431537592]
We consider a control system of the form $dot x = sum_i=1lF_i(x)u_i$, with linear dependence in the controls.
We use the corresponding flow to approximate the action of a diffeomorphism on a compact ensemble of points.
arXiv Detail & Related papers (2021-10-24T08:57:46Z) - On the Convexity of Discrete Time Covariance Steering in Stochastic
Linear Systems with Wasserstein Terminal Cost [1.1602089225841632]
We show that when the terminal state covariance is upper bounded, with respect to the L"owner partial order, our problem admits a unique global minimizing state feedback gain.
The results of this paper set the stage for the development of specialized control design tools.
arXiv Detail & Related papers (2021-03-25T03:24:52Z) - Gaussian Process-based Min-norm Stabilizing Controller for
Control-Affine Systems with Uncertain Input Effects and Dynamics [90.81186513537777]
We propose a novel compound kernel that captures the control-affine nature of the problem.
We show that this resulting optimization problem is convex, and we call it Gaussian Process-based Control Lyapunov Function Second-Order Cone Program (GP-CLF-SOCP)
arXiv Detail & Related papers (2020-11-14T01:27:32Z) - Direct Optimal Control Approach to Laser-Driven Quantum Particle
Dynamics [77.34726150561087]
We propose direct optimal control as a robust and flexible alternative to indirect control theory.
The method is illustrated for the case of laser-driven wavepacket dynamics in a bistable potential.
arXiv Detail & Related papers (2020-10-08T07:59:29Z) - Time-local optimal control for parameter estimation in the Gaussian
regime [68.8204255655161]
instantaneous control unitaries may be used to mitigate the decrease of information caused by an open dynamics.
A possible, locally optimal (in time) choice for such controls is the one that maximises the time-derivative of the quantum Fisher information.
arXiv Detail & Related papers (2020-01-10T16:24:31Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.