2,415 research outputs found
Physics-Informed Regularization of Deep Neural Networks
This paper presents a novel physics-informed regularization method for
training of deep neural networks (DNNs). In particular, we focus on the DNN
representation for the response of a physical or biological system, for which a
set of governing laws are known. These laws often appear in the form of
differential equations, derived from first principles, empirically-validated
laws, and/or domain expertise. We propose a DNN training approach that utilizes
these known differential equations in addition to the measurement data, by
introducing a penalty term to the training loss function to penalize divergence
form the governing laws. Through three numerical examples, we will show that
the proposed regularization produces surrogates that are physically
interpretable with smaller generalization errors, when compared to other common
regularization methods
Data-Driven Passivity-Based Control of Underactuated Robotic Systems
Classical control strategies for robotic systems are based on the idea that feedback control can be used to override the natural dynamics of the machines. Passivity-based control (Pbc) is a branch of nonlinear control theory that follows a similar approach, where the natural dynamics is modified based on the overall energy of the system. This method involves transforming a nonlinear control system, through a suitable control input, into another fictitious system that has desirable stability characteristics. The majority of Pbc techniques require the discovery of a reasonable storage function, which acts as a Lyapunov function candidate that can be used to certify stability.
There are several challenges in the design of a suitable storage function, including: 1) what a reasonable choice for the function is for a given control system, and 2) the control synthesis requires a closed-form solution to a set of nonlinear partial differential equations. The latter is in general difficult to overcome, especially for systems with high degrees of freedom, limiting the applicability of Pbc techniques.
A machine learning framework that automatically determines the storage function for underactuated robotic systems is introduced in this dissertation. This framework combines the expressive power of neural networks with the systematic methods of the Pbc paradigm, bridging the gap between controllers derived from learning algorithms and nonlinear control theory. A series of experiments demonstrates the efficacy and applicability of this framework for a family of underactuated robots
Gaining Insight into Determinants of Physical Activity using Bayesian Network Learning
Contains fulltext :
228326pre.pdf (preprint version ) (Open Access)
Contains fulltext :
228326pub.pdf (publisher's version ) (Open Access)BNAIC/BeneLearn 202
Convex Optimization-based Policy Adaptation to Compensate for Distributional Shifts
Many real-world systems often involve physical components or operating
environments with highly nonlinear and uncertain dynamics. A number of
different control algorithms can be used to design optimal controllers for such
systems, assuming a reasonably high-fidelity model of the actual system.
However, the assumptions made on the stochastic dynamics of the model when
designing the optimal controller may no longer be valid when the system is
deployed in the real-world. The problem addressed by this paper is the
following: Suppose we obtain an optimal trajectory by solving a control problem
in the training environment, how do we ensure that the real-world system
trajectory tracks this optimal trajectory with minimal amount of error in a
deployment environment. In other words, we want to learn how we can adapt an
optimal trained policy to distribution shifts in the environment. Distribution
shifts are problematic in safety-critical systems, where a trained policy may
lead to unsafe outcomes during deployment. We show that this problem can be
cast as a nonlinear optimization problem that could be solved using heuristic
method such as particle swarm optimization (PSO). However, if we instead
consider a convex relaxation of this problem, we can learn policies that track
the optimal trajectory with much better error performance, and faster
computation times. We demonstrate the efficacy of our approach on tracking an
optimal path using a Dubin's car model, and collision avoidance using both a
linear and nonlinear model for adaptive cruise control
Tasks Makyth Models: Machine Learning Assisted Surrogates for Tipping Points
We present a machine learning (ML)-assisted framework bridging manifold
learning, neural networks, Gaussian processes, and Equation-Free multiscale
modeling, for (a) detecting tipping points in the emergent behavior of complex
systems, and (b) characterizing probabilities of rare events (here,
catastrophic shifts) near them. Our illustrative example is an event-driven,
stochastic agent-based model (ABM) describing the mimetic behavior of traders
in a simple financial market. Given high-dimensional spatiotemporal data --
generated by the stochastic ABM -- we construct reduced-order models for the
emergent dynamics at different scales: (a) mesoscopic Integro-Partial
Differential Equations (IPDEs); and (b) mean-field-type Stochastic Differential
Equations (SDEs) embedded in a low-dimensional latent space, targeted to the
neighborhood of the tipping point. We contrast the uses of the different models
and the effort involved in learning them.Comment: 29 pages, 8 figures, 6 table
Deep Probabilistic Surrogate Networks for Universal Simulator Approximation
We present a framework for automatically structuring and training fast,
approximate, deep neural surrogates of existing stochastic simulators. Unlike
traditional approaches to surrogate modeling, our surrogates retain the
interpretable structure of the reference simulators. The particular way we
achieve this allows us to replace the reference simulator with the surrogate
when undertaking amortized inference in the probabilistic programming sense.
The fidelity and speed of our surrogates allow for not only faster "forward"
stochastic simulation but also for accurate and substantially faster inference.
We support these claims via experiments that involve a commercial
composite-materials curing simulator. Employing our surrogate modeling
technique makes inference an order of magnitude faster, opening up the
possibility of doing simulator-based, non-invasive, just-in-time parts quality
testing; in this case inferring safety-critical latent internal temperature
profiles of composite materials undergoing curing from surface temperature
profile measurements
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