Computer scientists use causal inference for reasoning. In causal inference, researchers are interested in finding the relationship between two observable events. In this paper, we will explore the first step towards finding causality using probabilistic fuzzy logic (PFL). We will also show that PFL is more precise than Pearl’s causality model.

Ideas and formalisms from far-from-equilibrium thermodynamics are ported to the context of stochastic computational processes, via following and extending Tadaki's algorithmic thermodynamics. A Principle of Maximum Algorithmic Caliber is proposed, providing guidance as to what computational processes one should hypothesize if one is provided constraints to work within. It is conjectured that, under suitable assumptions, computational processes obeying algorithmic Markov conditions will maximize algorithmic caliber. It is proposed that in accordance with this, real-world cognitive systems may operate in substantial part by modeling their environments and choosing their actions to be (approximate and compactly represented) algorithmic Markov networks. These ideas are suggested as potential early steps toward a general theory of the operation of pragmatic generally intelligent systems.

One group of researchers at The University of Texas at Austin is developing new "scientific machine learning" methods to address this challenge.

One group of researchers at The University of Texas at Austin is developing new "scientific machine learning" methods to address this challenge.

In this manuscript, we provide a structured and comprehensive overview of techniques to integrate machine learning with physics-based modeling. First, we provide a summary of application areas for which these approaches have been applied. Then, we describe classes of methodologies used to construct physics-guided machine learning models and hybrid physics-machine learning frameworks from a machine learning standpoint. With this foundation, we then provide a systematic organization of these existing techniques and discuss ideas for future research.

To understand changes in physical systems and facilitate decisions, explaining how model predictions are made is crucial. We use model-based interpretability, where models of physical systems are constructed by composing basic constructs that explain locally how energy is exchanged and transformed. We use the port Hamiltonian (p-H) formalism to describe the basic constructs that contain physically interpretable processes commonly found in the behavior of physical systems. We describe how we can build models out of the p-H constructs and how we can train them. In addition we show how we can impose physical properties such as dissipativity that ensure numerical stability of the training process. We give examples on how to build and train models for describing the behavior of two physical systems: the inverted pendulum and swarm dynamics. I. Introduction The necessity for interpretability comes from the fact that it is not always enough to train and model and get an answer, but is also important to understand why a particular answer was given. A simple but meaningful definition of model interpretability given in [17] relates this notion to the degree to which a human can understand the cause of a decision. In our case, since we care about models that describe the behavior of physical systems, we change the definition to the degree to which a human can understand the physical processes that cause a prediction. Throughout this paper we focus on physically-interpretable models: models that embed physical laws that explain how energy is transformed and exchanged in the system. A physically-interpretable model facilitates learning and updating the model when something unexpected happens. This update is done by finding an explanation for an unexpected event. For example, an electrical motor unexpectedly overheats and we ask ourselves: "Why is the motor overheating?".

Reduced-order models that accurately abstract high fidelity models and enable faster simulation is vital for real-time, model-based diagnosis applications. In this paper, we outline a novel hybrid modeling approach that combines machine learning inspired models and physics-based models to generate reduced-order models from high fidelity models. We are using such models for real-time diagnosis applications. Specifically, we have developed machine learning inspired representations to generate reduced order component models that preserve, in part, the physical interpretation of the original high fidelity component models. To ensure the accuracy, scalability and numerical stability of the learning algorithms when training the reduced-order models we use optimization platforms featuring automatic differentiation. Training data is generated by simulating the high-fidelity model. We showcase our approach in the context of fault diagnosis of a rail switch system. Three new model abstractions whose complexities are two orders of magnitude smaller than the complexity of the high fidelity model, both in the number of equations and simulation time are shown. The numerical experiments and results demonstrate the efficacy of the proposed hybrid modeling approach.

The human mind has a remarkable ability to associate causes with a specific event. From the outcome of an election to an object dropping on the floor, we are constantly associating chains of events that cause a specific effect. Neuropsychology refers to this cognitive ability as causal reasoning. Computer science and economics study a specific form of causal reasoning known as causal inference which focuses on exploring relationships between two observed variables. Over the years, machine learning has produced many methods for causal inference but they remain mostly difficult to use in mainstream applications.

Causal structure-discovery techniques usually assume that all causes of more than one variable are observed. This is the so-called causal sufficiency assumption. In practice, it is untestable, and often violated. In this paper, we present an efficient causal structure-learning algorithm, suited for causally insufficient data. Similar to algorithms such as IC* and FCI, the proposed approach drops the causal sufficiency assumption and learns a structure that indicates (potential) latent causes for pairs of observed variables.

There is growing interest in combining model-free and model-based approaches in reinforcement learning with the goal of achieving the high performance of model-free algorithms with low sample complexity. This is difficult because an imperfect dynamics model can degrade the performance of the learning algorithm, and in sufficiently complex environments, the dynamics model will always be imperfect. As a result, a key challenge is to combine model-based approaches with model-free learning in such a way that errors in the model do not degrade performance. We propose stochastic ensemble value expansion (STEVE), a novel model-based technique that addresses this issue. By dynamically interpolating between model rollouts of various horizon lengths, STEVE ensures that the model is only utilized when doing so does not introduce significant errors.