A comparison of Single- and Double-generator formalisms for Thermodynamics-Informed Neural Networks

The development of inductive biases has been shown to be a very effective way to increase the accuracy and robustness of neural networks, particularly when they are used to predict physical phenomena. These biases significantly increase the certainty of predictions, decrease the error made and allow considerably smaller datasets to be used. There are a multitude of methods in the literature to develop these biases. One of the most effective ways, when dealing with physical phenomena, is to introduce physical principles of recognised validity into the network architecture. The problem becomes more complex without knowledge of the physical principles governing the phenomena under study. A very interesting possibility then is to turn to the principles of thermodynamics, which are universally valid, regardless of the level of abstraction of the description sought for the phenomenon under study. To ensure compliance with the principles of thermodynamics, there are formulations that have a long tradition in many branches of science. In the field of rheology, for example, two main types of formalisms are used to ensure compliance with these principles: one-generator and two-generator formalisms. In this paper we study the advantages and disadvantages of each, using classical problems with known solutions and synthetic data.

Thermodynamics-informed super-resolution of scarce temporal dynamics data

We present a method to increase the resolution of measurements of a physical system and subsequently predict its time evolution using thermodynamics-aware neural networks. Our method uses adversarial autoencoders, which reduce the dimensionality of the full order model to a set of latent variables that are enforced to match a prior, for example a normal distribution. Adversarial autoencoders are seen as generative models, and they can be trained to generate high-resolution samples from low-resoution inputs, meaning they can address the so-called super-resolution problem. Then, a second neural network is trained to learn the physical structure of the latent variables and predict their temporal evolution. This neural network is known as an structure-preserving neural network. It learns the metriplectic-structure of the system and applies a physical bias to ensure that the first and second principles of thermodynamics are fulfilled. The integrated trajectories are decoded to their original dimensionality, as well as to the higher dimensionality space produced by the adversarial autoencoder and they are compared to the ground truth solution. The method is tested with two examples of flow over a cylinder, where the fluid properties are varied between both examples.

Port-metriplectic neural networks: thermodynamics-informed machine learning of complex physical systems

We develop inductive biases for the machine learning of complex physical systems based on the port-Hamiltonian formalism. To satisfy by construction the principles of thermodynamics in the learned physics (conservation of energy, non-negative entropy production), we modify accordingly the port-Hamiltonian formalism so as to achieve a port-metriplectic one. We show that the constructed networks are able to learn the physics of complex systems by parts, thus alleviating the burden associated to the experimental characterization and posterior learning process of this kind of systems. Predictions can be done, however, at the scale of the complete system. Examples are shown on the performance of the proposed technique.

Thermodynamics-informed neural networks for physically realistic mixed reality

The imminent impact of immersive technologies in society urges for active research in real-time and interactive physics simulation for virtual worlds to be realistic. In this context, realistic means to be compliant to the laws of physics. In this paper we present a method for computing the dynamic response of (possibly non-linear and dissipative) deformable objects induced by real-time user interactions in mixed reality using deep learning. The graph-based architecture of the method ensures the thermodynamic consistency of the predictions, whereas the visualization pipeline allows a natural and realistic user experience. Two examples of virtual solids interacting with virtual or physical solids in mixed reality scenarios are provided to prove the performance of the method.

Thermodynamics of learning physical phenomena

Thermodynamics could be seen as an expression of physics at a high epistemic level. As such, its potential as an inductive bias to help machine learning procedures attain accurate and credible predictions has been recently realized in many fields. We review how thermodynamics provides helpful insights in the learning process. At the same time, we study the influence of aspects such as the scale at which a given phenomenon is to be described, the choice of relevant variables for this description or the different techniques available for the learning process.

Physics-informed Reinforcement Learning for Perception and Reasoning about Fluids

Learning and reasoning about physical phenomena is still a challenge in robotics development, and computational sciences play a capital role in the search for accurate methods able to provide explanations for past events and rigorous forecasts of future situations. We propose a physics-informed reinforcement learning strategy for fluid perception and reasoning from observations. As a model problem, we take the sloshing phenomena of different fluids contained in a glass. Starting from full-field and high-resolution synthetic data for a particular fluid, we develop a method for the tracking (perception) and analysis (reasoning) of any previously unseen liquid whose free surface is observed with a commodity camera. This approach demonstrates the importance of physics and knowledge not only in data-driven (grey box) modeling but also in the correction for real physics adaptation in low data regimes and partial observations of the dynamics. The method here presented is extensible to other domains such as the development of cognitive digital twins, able to learn from observation of phenomena for which they have not been trained explicitly.

Thermodynamics-informed graph neural networks

In this paper we present a deep learning method to predict the time evolution of dissipative dynamical systems. We propose using both geometric and thermodynamic inductive biases to improve accuracy and generalization of the resulting integration scheme. The first is achieved with Graph Neural Networks, which induces a non-Euclidean geometrical prior and permutation invariant node and edge update functions. The second bias is forced by learning the GENERIC structure of the problem, an extension of the Hamiltonian formalism, to model more general non-conservative dynamics. Several examples are provided in both Eulerian and Lagrangian description in the context of fluid and solid mechanics respectively.

Monitoring weeder robots and anticipating their functioning by using advanced topological data analysis

The present paper aims at analyzing the topological content of the complex trajectories that weeder-autonomous robots follow in operation. We will prove that the topological descriptors of these trajectories are affected by the robot environment as well as by the robot state, with respect to maintenance operations. Topological Data Analysis will be used for extracting the trajectory descriptors, based on homology persistence. Then, appropriate metrics will be applied in order to compare that topological representation of the trajectories, for classifying them or for making efficient pattern recognition.

Physics perception in sloshing scenes with guaranteed thermodynamic consistency

Physics perception very often faces the problem that only limited data or partial measurements on the scene are available. In this work, we propose a strategy to learn the full state of sloshing liquids from measurements of the free surface. Our approach is based on recurrent neural networks (RNN) that project the limited information available to a reduced-order manifold so as to not only reconstruct the unknown information, but also to be capable of performing fluid reasoning about future scenarios in real time. To obtain physically consistent predictions, we train deep neural networks on the reduced-order manifold that, through the employ of inductive biases, ensure the fulfillment of the principles of thermodynamics. RNNs learn from history the required hidden information to correlate the limited information with the latent space where the simulation occurs. Finally, a decoder returns data back to the high-dimensional manifold, so as to provide the user with insightful information in the form of augmented reality. This algorithm is connected to a computer vision system to test the performance of the proposed methodology with real information, resulting in a system capable of understanding and predicting future states of the observed fluid in real-time.

Learning stable reduced-order models for hybrid twins

The concept of Hybrid Twin (HT) has recently received a growing interest thanks to the availability of powerful machine learning techniques. This twin concept combines physics-based models within a model-order reduction framework-to obtain real-time feedback rates-and data science. Thus, the main idea of the HT is to develop on-the-fly data-driven models to correct possible deviations between measurements and physics-based model predictions. This paper is focused on the computation of stable, fast and accurate corrections in the Hybrid Twin framework. Furthermore, regarding the delicate and important problem of stability, a new approach is proposed, introducing several sub-variants and guaranteeing a low computational cost as well as the achievement of a stable time-integration.