Reza Khodayi-mehr

Reza Khodayi-mehr, Matthew W. Urban, Michael M. Zavlanos et al.

In this paper, we propose Plane Wave Elastography (PWE), a novel ultrasound shear wave elastography (SWE) approach. Currently, commercial methods for SWE rely on directional filtering based on the prior knowledge of the wave propagation direction, to remove complicated wave patterns formed due to reflection and refraction. The result is a set of decomposed directional waves that are separately analyzed to construct shear modulus fields that are then combined through compounding. Instead, PWE relies on a rigorous representation of the wave propagation using the frequency-domain scalar wave equation to automatically select appropriate propagation directions and simultaneously reconstruct shear modulus fields. Specifically, assuming a homogeneous, isotropic, incompressible, linear-elastic medium, we represent the solution of the wave equation using a linear combination of plane waves propagating in arbitrary directions. Given this closed-form solution, we formulate the SWE problem as a nonlinear least-squares optimization problem which can be solved very efficiently. Through numerous phantom studies, we show that PWE can handle complicated waveforms without prior filtering and is competitive with state-of-the-art that requires prior filtering based on the knowledge of propagation directions.

Reza Khodayi-Mehr, Michael M. Zavlanos

In this paper we propose a new model-based unsupervised learning method, called VarNet, for the solution of partial differential equations (PDEs) using deep neural networks (NNs). Particularly, we propose a novel loss function that relies on the variational (integral) form of PDEs as apposed to their differential form which is commonly used in the literature. Our loss function is discretization-free, highly parallelizable, and more effective in capturing the solution of PDEs since it employs lower-order derivatives and trains over measure non-zero regions of space-time. Given this loss function, we also propose an approach to optimally select the space-time samples, used to train the NN, that is based on the feedback provided from the PDE residual. The models obtained using VarNet are smooth and do not require interpolation. They are also easily differentiable and can directly be used for control and optimization of PDEs. Finally, VarNet can straight-forwardly incorporate parametric PDE models making it a natural tool for model order reduction (MOR) of PDEs. We demonstrate the performance of our method through extensive numerical experiments for the advection-diffusion PDE as an important case-study.

Reza Khodayi-mehr, Michael M. Zavlanos

We consider the problem of mass transport cloaking using mobile robots. The robots move along a predefined curve that encloses a safe zone and carry sources that collectively counteract a chemical agent released in the environment. The goal is to steer the mass flux around a desired region so that it remains unaffected by the external concentration. We formulate the problem of controlling the robot positions and release rates as a PDE-constrained optimization, where the propagation of the chemical is modeled by the advection-diffusion (AD) PDE. We use a neural network (NN) to approximate the solution of the PDE. Particularly, we propose a novel loss function for the NN that utilizes the variational form of the AD-PDE and allows us to reformulate the planning problem as an unsupervised model-based learning problem. Our loss function is discretization-free and highly parallelizable. Unlike passive cloaking methods that use metamaterials to steer the mass flux, our method is the first to use mobile robots to actively control the concentration levels and create safe zones independent of environmental conditions. We demonstrate the performance of our method in simulations.

Reza Khodayi-mehr, Michael M. Zavlanos

We propose a physics-based method to learn environmental fields (EFs) using a mobile robot. Common purely data-driven methods require prohibitively many measurements to accurately learn such complex EFs. Alternatively, physics-based models provide global knowledge of EFs but require experimental validation, depend on uncertain parameters, and are intractable for mobile robots. To address these challenges, we propose a Bayesian framework to select the most likely physics-based models of EFs in real-time, from a pool of numerical solutions generated offline as a function of the uncertain parameters. Specifically, we focus on turbulent flow fields and utilize Gaussian processes (GPs) to construct statistical models for them, using the pool of numerical solutions to inform their prior mean. To incorporate flow measurements into these GPs, we control a custom-built mobile robot through a sequence of waypoints that maximize the information content of the measurements. We experimentally demonstrate that our proposed framework constructs a posterior distribution of the flow field that better approximates the real flow compared to the prior numerical solutions and purely data-driven methods.

Reza Khodayi-mehr, Yiannis Kantaros, Michael M. Zavlanos

This paper considers the problem of distributed state estimation using multi-robot systems. The robots have limited communication capabilities and, therefore, communicate their measurements intermittently only when they are physically close to each other. To decrease the distance that the robots need to travel only to communicate, we divide them into small teams that can communicate at different locations to share information and update their beliefs. Then, we propose a new distributed scheme that combines (i) communication schedules that ensure that the network is intermittently connected, and (ii) sampling-based motion planning for the robots in every team with the objective to collect optimal measurements and decide a location for those robots to communicate. To the best of our knowledge, this is the first distributed state estimation framework that relaxes all network connectivity assumptions, and controls intermittent communication events so that the estimation uncertainty is minimized. We present simulation results that demonstrate significant improvement in estimation accuracy compared to methods that maintain an end-to-end connected network for all time.

Reza Khodayi-mehr, Wilkins Aquino, Michael M. Zavlanos

We consider the problem of Active Source Identification (ASI) in steady-state Advection-Diffusion (AD) transport systems. Unlike existing bio-inspired heuristic methods, we propose a model-based method that employs the AD-PDE to capture the transport phenomenon. Specifically, we formulate the Source Identification (SI) problem as a PDE-constrained optimization problem in function spaces. To obtain a tractable solution, we reduce the dimension of the concentration field using Proper Orthogonal Decomposition and approximate the unknown source field using nonlinear basis functions, drastically decreasing the number of unknowns. Moreover, to collect the concentration measurements, we control a robot sensor through a sequence of waypoints that maximize the smallest eigenvalue of the Fisher Information matrix of the unknown source parameters. Specifically, after every new measurement, a SI problem is solved to obtain a source estimate that is used to determine the next waypoint. We show that our algorithm can efficiently identify sources in complex AD systems and non-convex domains, in simulation and experimentally. This is the first time that PDEs are used for robotic SI in practice.