Nonlinear Model Reduction of Stochastic Microdynamics

This thesis presents a nonlinear model reduction procedure for stochastic microdynamics models that possess mesoscale separation between fast and slow dynamics. Model reduction procedures typically reduce the dimension of deterministic dynamical systems through linear projection operators which offer limited compression capabilities for nonlinear systems. On the other hand, deep neural networks provide a class of nonlinear transformations for regression that can approximate arbitrarily complex functions. The approach developed in this thesis attempts to carry out nonlinear model reduction of stochastic models using deep neural networks to approximate a transformation onto reduced coordinates taken to be the parameters of the network. The stochasticity of the microdynamics is inherited by the reduced, mesoscale model by viewing the parameters as stochastic processes. Moderate time scale separation suggests that non-Gaussian behavior must be considered in contrast with the convergence to Gaussian noise in the limit of infinite timescale separation provided by homogenization theory. This thesis considers several approaches for modeling the stochastic processes concluding with an information geometric strategy for estimating probability distribution functions. The procedure is applied to protein folding within molecular dynamics simulations, a widely used technique to model large collections of atoms which interact through nonlinear forces and are driven by a stochastic heat bath. Protein folding occurs on a larger, mesoscale with respect to the timescale of numerical integration.Doctor of Philosoph

Path planning and control of flying robots with account of human’s safety perception

In this dissertation, a framework for planning and control of flying robot with the account of human’s safety perception is presented. The framework enables the flying robot to consider the human’s perceived safety in path planning. First, a data-driven model of the human’s safety perception is estimated from human’s test data using a virtual reality environment. A hidden Markov model (HMM) is considered for estimation of latent variables, as user’s attention, intention, and emotional state. Then, an optimal motion planner generates a trajectory, parameterized in Bernstein polynomials, which minimizes the cost related to the mission objectives while satisfying the constraints on the predicted human’s safety perception. Using Model Predictive Path Integral (MPPI) framework, the algorithm is possible to execute in real-time measuring the human’s spatial position and the changes in the environment. A HMM-based Q-learning is considered for computing the online optimal policy. The HMM-based Q-learning estimates the hidden state of the human in interactions with the robot. The state estimator in the HMM-based Q-learning infers the hidden states of the human based on past observations and actions. The convergence of the HMM-based Q-learning for a partially observable Markov decision process (POMDP) with finite state space is proved using stochastic approximation technique. As future research direction one can consider to use recurrent neural networks to estimate the hidden state in continuous state space. The analysis of the convergence of the HMM-based Q-learning algorithm suggests that the training of the recurrent neural network needs to consider both the state estimation accuracy and the optimality principle

Computational intelligence approaches to robotics, automation, and control [Volume guest editors]

No abstract available

Temporal BYY Encoding, Markovian State Spaces, and Space Dimension Determination

As a complementary to those temporal coding approaches of the current major stream, this paper aims at the Markovian state space temporal models from the perspective of the temporal Bayesian Ying-Yang (BYY) learning with both new insights and new results on not only the discrete state featured Hidden Markov model and extensions but also the continuous state featured linear state spaces and extensions, especially with a new learning mechanism that makes selection of the state number or the dimension of state space either automatically during adaptive learning or subsequently after learning via model selection criteria obtained from this mechanism. Experiments are demonstrated to show how the proposed approach works

A comparison of the CAR and DAGAR spatial random effects models with an application to diabetics rate estimation in Belgium

When hierarchically modelling an epidemiological phenomenon on a finite collection of sites in space, one must always take a latent spatial effect into account in order to capture the correlation structure that links the phenomenon to the territory. In this work, we compare two autoregressive spatial models that can be used for this purpose: the classical CAR model and the more recent DAGAR model. Differently from the former, the latter has a desirable property: its ρ parameter can be naturally interpreted as the average neighbor pair correlation and, in addition, this parameter can be directly estimated when the effect is modelled using a DAGAR rather than a CAR structure. As an application, we model the diabetics rate in Belgium in 2014 and show the adequacy of these models in predicting the response variable when no covariates are available

A Statistical Approach to the Alignment of fMRI Data

Multi-subject functional Magnetic Resonance Image studies are critical. The anatomical and functional structure varies across subjects, so the image alignment is necessary. We define a probabilistic model to describe functional alignment. Imposing a prior distribution, as the matrix Fisher Von Mises distribution, of the orthogonal transformation parameter, the anatomical information is embedded in the estimation of the parameters, i.e., penalizing the combination of spatially distant voxels. Real applications show an improvement in the classification and interpretability of the results compared to various functional alignment methods

New Directions for Contact Integrators

Contact integrators are a family of geometric numerical schemes which guarantee the conservation of the contact structure. In this work we review the construction of both the variational and Hamiltonian versions of these methods. We illustrate some of the advantages of geometric integration in the dissipative setting by focusing on models inspired by recent studies in celestial mechanics and cosmology.Comment: To appear as Chapter 24 in GSI 2021, Springer LNCS 1282