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Reinforcement learning-based estimation for partial differential equations

arXiv.org Artificial Intelligence

We evaluate the state estimation performance of the RL-ROE for systems governed by the Burgers equation and Navier-Stokes equations. For each system, we first compute various solution trajectories corresponding to different physical parameter values, which we use to construct the ROM and train the RL-ROE following the procedure outlined in Section 2.4. The trained RL-ROE is finally deployed online and compared against a time-dependent Kalman filter constructed from the same ROM, which we refer to as KF-ROE. The KF-ROE is given by equations (3a) and (4), with the calculation of the time-varying Kalman gain detailed in Appendix C of the supplementary materials. Before proceeding to the results, we discuss our choice of baseline. The ensemble Kalman filter and 4D-Var are two estimation techniques for high-dimensional systems such as those governed by PDEs (Lorenc, 2003). Although they are commonly employed for data assimilation in numerical weather prediction, they require large computational resources since they involve repeated solutions of the high-dimensional dynamics (1). Thus, they are not applicable in the context of embedded control systems, whose limited resources call for an inexpensive model such as the ROM (2). Since the ROM that we consider has linear dynamics, extensions of the Kalman filter for nonlinear dynamics such as the extended or unscented Kalman filters (Wan & Van Der Merwe, 2000; Julier & Uhlmann, 2004) are not relevant, and the vanilla Kalman filter remains the best choice of baseline.


Likelihood-based generalization of Markov parameter estimation and multiple shooting objectives in system identification

arXiv.org Artificial Intelligence

This paper considers the problem of system identification (ID) of linear and nonlinear non-autonomous systems from noisy and sparse data. We propose and analyze an objective function derived from a Bayesian formulation for learning a hidden Markov model with stochastic dynamics. We then analyze this objective function in the context of several state-of-the-art approaches for both linear and nonlinear system ID. In the former, we analyze least squares approaches for Markov parameter estimation, and in the latter, we analyze the multiple shooting approach. We demonstrate the limitations of the optimization problems posed by these existing methods by showing that they can be seen as special cases of the proposed optimization objective under certain simplifying assumptions: conditional independence of data and zero model error. Furthermore, we observe that our proposed approach has improved smoothness and inherent regularization that make it well-suited for system ID and provide mathematical explanations for these characteristics' origins. Finally, numerical simulations demonstrate a mean squared error over 8.7 times lower compared to multiple shooting when data are noisy and/or sparse. Moreover, the proposed approach can identify accurate and generalizable models even when there are more parameters than data or when the underlying system exhibits chaotic behavior.


Plan To Predict: Learning an Uncertainty-Foreseeing Model for Model-Based Reinforcement Learning

arXiv.org Artificial Intelligence

In Model-based Reinforcement Learning (MBRL), model learning is critical since an inaccurate model can bias policy learning via generating misleading samples. However, learning an accurate model can be difficult since the policy is continually updated and the induced distribution over visited states used for model learning shifts accordingly. Prior methods alleviate this issue by quantifying the uncertainty of model-generated samples. However, these methods only quantify the uncertainty passively after the samples were generated, rather than foreseeing the uncertainty before model trajectories fall into those highly uncertain regions. The resulting low-quality samples can induce unstable learning targets and hinder the optimization of the policy. Moreover, while being learned to minimize one-step prediction errors, the model is generally used to predict for multiple steps, leading to a mismatch between the objectives of model learning and model usage. To this end, we propose \emph{Plan To Predict} (P2P), an MBRL framework that treats the model rollout process as a sequential decision making problem by reversely considering the model as a decision maker and the current policy as the dynamics. In this way, the model can quickly adapt to the current policy and foresee the multi-step future uncertainty when generating trajectories. Theoretically, we show that the performance of P2P can be guaranteed by approximately optimizing a lower bound of the true environment return. Empirical results demonstrate that P2P achieves state-of-the-art performance on several challenging benchmark tasks.


DECISIVE Test Methods Handbook: Test Methods for Evaluating sUAS in Subterranean and Constrained Indoor Environments, Version 1.1

arXiv.org Artificial Intelligence

This handbook outlines all test methods developed under the Development and Execution of Comprehensive and Integrated Subterranean Intelligent Vehicle Evaluations (DECISIVE) project by the University of Massachusetts Lowell for evaluating small unmanned aerial systems (sUAS) performance in subterranean and constrained indoor environments, spanning communications, field readiness, interface, obstacle avoidance, navigation, mapping, autonomy, trust, and situation awareness. For sUAS deployment in subterranean and constrained indoor environments, this puts forth two assumptions about applicable sUAS to be evaluated using these test methods: (1) able to operate without access to GPS signal, and (2) width from prop top to prop tip does not exceed 91 cm (36 in) wide (i.e., can physically fit through a typical doorway, although successful navigation through is not guaranteed). All test methods are specified using a common format: Purpose, Summary of Test Method, Apparatus and Artifacts, Equipment, Metrics, Procedure, and Example Data. All test methods are designed to be run in real-world environments (e.g., MOUT sites) or using fabricated apparatuses (e.g., test bays built from wood, or contained inside of one or more shipping containers).


Why a Social License is Needed for AI

#artificialintelligence

If business wants to use AI at scale, adhering to the technical guidelines for responsible AI development isn't enough. It must obtain society's explicit approval to deploy the technology. Six years ago, in March 2016, Microsoft Corporation launched an experimental AI-based chatbot, TayTweets, whose Twitter handle was @TayandYou. Tay, an acronym for "thinking about you," mimicked a 19-year-old American girl online, so the digital giant could showcase the speed at which AI can learn when it interacts with human beings. Living up to its description as "AI with zero chill," Tay started off replying cheekily to Twitter users and turning photographs into memes. Some topics were off limits, though; Microsoft had trained Tay not to comment on societal issues such as Black Lives Matter. Soon enough, a group of Twitter users targeted Tay with a barrage of tweets about controversial issues such as the Holocaust and Gamergate. They goaded the chatbot into replying with racist and sexually charged responses, exploiting its repeat-after-me capability. Realizing that Tay was reacting like IBM's Watson, which started using profanity after perusing the online Urban Dictionary, Microsoft was quick to delete the first inflammatory tweets. Less than 16 hours and more than 100,000 tweets later, the digital giant shut down Tay.


Al Gore explains global AI program that is spying on thousands of facilities to monitor emissions

FOX News

Former Vice President Al Gore on Thursday outlined a global effort run by "machine-learning" artificial intelligence is essentially spying on individual facilities in every country in the world to measure their emissions of greenhouse gases and target the world's largest emitters. At the World Economic Forum in Davos, Switzerland, Gore formally introduced attendees to the initiative known as Climate Tracking Real-Time Atmospheric Carbon Emissions, or Climate TRACE. The initiative has led to a website that allows for real-time tracking of emissions in any area of the world, which Gore said is allowing climate activists, reporters and others to identify high-priority industries and regions for emissions reduction programs. "It's a non-profit coalition that uses artificial intelligence to process data from 300 existing satellites and from 30,000 land, sea and air base sensors and multiple internet data streams to use artificial intelligence to create machine-learning algorithms to zoom in on every single significant source of greenhouse gas (GHG) pollution," he said of Climate TRACE. Gore showed how Climate TRACE uses these inputs to zoom in on specific facilities and assess how much they contribute to GHG emissions.


Here are the 5 biggest innovations to expect in 2023

#artificialintelligence

We may be a mere 23 years into the century but already it has been a doozy. In 2022, we saw impressive technological feats, including a fusion energy breakthrough, the first successful all-electric passenger plane test, and the release of bivalent Covid-19 booster vaccines. As we enter into 2023, what can we expect? At Inverse, we aren't in the business of fortune-telling, but the innovations we saw in the last 12 months can help us predict what might be in store for the next -- from driver-free transportation to commercial space exploration to (finally) clean energy for all This year will usher in more affordable EVs, allowing a bigger chunk of the population to drive sustainably. For example, GM is rolling out cheaper models that run for around $30,000, expanding the choices for drivers on a budget.


Computers that power self-driving cars could be a huge driver of global carbon emissions

#artificialintelligence

In the future, the energy needed to run the powerful computers on board a global fleet of autonomous vehicles could generate as many greenhouse gas emissions as all the data centers in the world today. That is one key finding of a new study from MIT researchers that explored the potential energy consumption and related carbon emissions if autonomous vehicles are widely adopted. The data centers that house the physical computing infrastructure used for running applications are widely known for their large carbon footprint: They currently account for about 0.3 percent of global greenhouse gas emissions, or about as much carbon as the country of Argentina produces annually, according to the International Energy Agency. Realizing that less attention has been paid to the potential footprint of autonomous vehicles, the MIT researchers built a statistical model to study the problem. They determined that 1 billion autonomous vehicles, each driving for one hour per day with a computer consuming 840 watts, would consume enough energy to generate about the same amount of emissions as data centers currently do.


Artificial intelligence helps build better lithium batteries

#artificialintelligence

How can artificial intelligence bring us closer to a more efficient, more easily recycled and better batteries? Recharge Industries has just announced it will build a $300 million lithium ion battery "gigafactory" in Geelong, Victoria, targeting 2 GWh of production a year in 2024 and 6 GWh by 2026. Lithium ion batteries are in growing demand worldwide with the expected skyrocketing introduction of electric vehicles. But beyond this news, Recharge Industries will also partner with Deakin University's Applied Artificial Intelligence Institute (A2I2) in Geelong to use artificial intelligence to build a better battery. The idea of using AI to improve batteries is not new, but A2I2 has created an operating system specifically designed for the lithium ion battery project, to speed up the design process.


A Metalearning Approach for Physics-Informed Neural Networks (PINNs): Application to Parameterized PDEs

arXiv.org Artificial Intelligence

Physics-informed neural networks (PINNs) as a means of discretizing partial differential equations (PDEs) are garnering much attention in the Computational Science and Engineering (CS&E) world. At least two challenges exist for PINNs at present: an understanding of accuracy and convergence characteristics with respect to tunable parameters and identification of optimization strategies that make PINNs as efficient as other computational science tools. The cost of PINNs training remains a major challenge of Physics-informed Machine Learning (PiML) - and, in fact, machine learning (ML) in general. This paper is meant to move towards addressing the latter through the study of PINNs on new tasks, for which parameterized PDEs provides a good testbed application as tasks can be easily defined in this context. Following the ML world, we introduce metalearning of PINNs with application to parameterized PDEs. By introducing metalearning and transfer learning concepts, we can greatly accelerate the PINNs optimization process. We present a survey of model-agnostic metalearning, and then discuss our model-aware metalearning applied to PINNs as well as implementation considerations and algorithmic complexity. We then test our approach on various canonical forward parameterized PDEs that have been presented in the emerging PINNs literature.