Constrained Recurrent Bayesian Forecasting for Crack Propagation

Predictive maintenance of railway infrastructure, especially railroads, is essential to ensure safety. However, accurate prediction of crack evolution represents a major challenge due to the complex interactions between intrinsic and external factors, as well as measurement uncertainties. Effective modeling requires a multidimensional approach and a comprehensive understanding of these dynamics and uncertainties. Motivated by an industrial use case based on collected real data containing measured crack lengths, this paper introduces a robust Bayesian multi-horizon approach for predicting the temporal evolution of crack lengths on rails. This model captures the intricate interplay between various factors influencing crack growth. Additionally, the Bayesian approach quantifies both epistemic and aleatoric uncertainties, providing a confidence interval around predictions. To enhance the model's reliability for railroad maintenance, specific constraints are incorporated. These constraints limit non-physical crack propagation behavior and prioritize safety. The findings reveal a trade-off between prediction accuracy and constraint compliance, highlighting the nuanced decision-making process in model training. This study offers insights into advanced predictive modeling for dynamic temporal forecasting, particularly in railway maintenance, with potential applications in other domains.

NeurIPS 2024 ML4CFD Competition: Harnessing Machine Learning for Computational Fluid Dynamics in Airfoil Design

The integration of machine learning (ML) techniques for addressing intricate physics problems is increasingly recognized as a promising avenue for expediting simulations. However, assessing ML-derived physical models poses a significant challenge for their adoption within industrial contexts. This competition is designed to promote the development of innovative ML approaches for tackling physical challenges, leveraging our recently introduced unified evaluation framework known as Learning Industrial Physical Simulations (LIPS). Building upon the preliminary edition held from November 2023 to March 2024, this iteration centers on a task fundamental to a well-established physical application: airfoil design simulation, utilizing our proposed AirfRANS dataset. The competition evaluates solutions based on various criteria encompassing ML accuracy, computational efficiency, Out-Of-Distribution performance, and adherence to physical principles. Notably, this competition represents a pioneering effort in exploring ML-driven surrogate methods aimed at optimizing the trade-off between computational efficiency and accuracy in physical simulations. Hosted on the Codabench platform, the competition offers online training and evaluation for all participating solutions.

ML4PhySim : Machine Learning for Physical Simulations Challenge (The airfoil design)

The use of machine learning (ML) techniques to solve complex physical problems has been considered recently as a promising approach. However, the evaluation of such learned physical models remains an important issue for industrial use. The aim of this competition is to encourage the development of new ML techniques to solve physical problems using a unified evaluation framework proposed recently, called Learning Industrial Physical Simulations (LIPS). We propose learning a task representing a well-known physical use case: the airfoil design simulation, using a dataset called AirfRANS. The global score calculated for each submitted solution is based on three main categories of criteria covering different aspects, namely: ML-related, Out-Of-Distribution, and physical compliance criteria. To the best of our knowledge, this is the first competition addressing the use of ML-based surrogate approaches to improve the trade-off computational cost/accuracy of physical simulation.The competition is hosted by the Codabench platform with online training and evaluation of all submitted solutions.

Interpretable learning of effective dynamics for multiscale systems

The modeling and simulation of high-dimensional multiscale systems is a critical challenge across all areas of science and engineering. It is broadly believed that even with today's computer advances resolving all spatiotemporal scales described by the governing equations remains a remote target. This realization has prompted intense efforts to develop model order reduction techniques. In recent years, techniques based on deep recurrent neural networks have produced promising results for the modeling and simulation of complex spatiotemporal systems and offer large flexibility in model development as they can incorporate experimental and computational data. However, neural networks lack interpretability, which limits their utility and generalizability across complex systems. Here we propose a novel framework of Interpretable Learning Effective Dynamics (iLED) that offers comparable accuracy to state-of-the-art recurrent neural network-based approaches while providing the added benefit of interpretability. The iLED framework is motivated by Mori-Zwanzig and Koopman operator theory, which justifies the choice of the specific architecture. We demonstrate the effectiveness of the proposed framework in simulations of three benchmark multiscale systems. Our results show that the iLED framework can generate accurate predictions and obtain interpretable dynamics, making it a promising approach for solving high-dimensional multiscale systems.

Rail Crack Propagation Forecasting Using Multi-horizons RNNs

The prediction of rail crack length propagation plays a crucial role in the maintenance and safety assessment of materials and structures. Traditional methods rely on physical models and empirical equations such as Paris law, which often have limitations in capturing the complex nature of crack growth. In recent years, machine learning techniques, particularly Recurrent Neural Networks (RNNs), have emerged as promising methods for time series forecasting. They allow to model time series data, and to incorporate exogenous variables into the model. The proposed approach involves collecting real data on the French rail network that includes historical crack length measurements, along with relevant exogenous factors that may influence crack growth. First, a pre-processing phase was performed to prepare a consistent data set for learning. Then, a suitable Bayesian multi-horizons recurrent architecture was designed to model the crack propagation phenomenon. Obtained results show that the Multi-horizons model outperforms state-of-the-art models such as LSTM and GRU.

Hybrid data driven/thermal simulation model for comfort assessment

Machine learning models improve the speed and quality of physical models. However, they require a large amount of data, which is often difficult and costly to acquire. Predicting thermal comfort, for example, requires a controlled environment, with participants presenting various characteristics (age, gender, ...). This paper proposes a method for hybridizing real data with simulated data for thermal comfort prediction. The simulations are performed using Modelica Language. A benchmarking study is realized to compare different machine learning methods. Obtained results look promising with an F1 score of 0.999 obtained using the random forest model.

Meta-Learning for Airflow Simulations with Graph Neural Networks

The field of numerical simulation is of significant importance for the design and management of real-world systems, with partial differential equations (PDEs) being a commonly used mathematical modeling tool. However, solving PDEs remains still a challenge, as commonly used traditional numerical solvers often require high computational costs. As a result, data-driven methods leveraging machine learning (more particularly Deep Learning) algorithms have been increasingly proposed to learn models that can predict solutions to complex PDEs, such as those arising in computational fluid dynamics (CFD). However, these methods are known to suffer from poor generalization performance on out-of-distribution (OoD) samples, highlighting the need for more efficient approaches. To this end, we present a meta-learning approach to enhance the performance of learned models on OoD samples. Specifically, we set the airflow simulation in CFD over various airfoils as a meta-learning problem, where each set of examples defined on a single airfoil shape is treated as a separate task. Through the use of model-agnostic meta-learning (MAML), we learn a meta-learner capable of adapting to new tasks, i.e., previously unseen airfoil shapes, using only a small amount of task-specific data. We experimentally demonstrate the efficiency of the proposed approach for improving the OoD generalization performance of learned models while maintaining efficiency.

Continuous Methods : Adaptively intrusive reduced order model closure

Reduced order modeling methods are often used as a mean to reduce simulation costs in industrial applications. Despite their computational advantages, reduced order models (ROMs) often fail to accurately reproduce complex dynamics encountered in real life applications. To address this challenge, we leverage NeuralODEs to propose a novel ROM correction approach based on a time-continuous memory formulation. Finally, experimental results show that our proposed method provides a high level of accuracy while retaining the low computational costs inherent to reduced models.

Continuous Methods : Hamiltonian Domain Translation

This paper proposes a novel approach to domain translation. Leveraging established parallels between generative models and dynamical systems, we propose a reformulation of the Cycle-GAN architecture. By embedding our model with a Hamiltonian structure, we obtain a continuous, expressive and most importantly invertible generative model for domain translation.

CD-ROM: Complementary Deep-Reduced Order Model

Model order reduction through the POD-Galerkin method can lead to dramatic gains in terms of computational efficiency in solving physical problems. However, the applicability of the method to non linear high-dimensional dynamical systems such as the Navier-Stokes equations has been shown to be limited, producing inaccurate and sometimes unstable models. This paper proposes a closure modeling approach for classical POD-Galerkin reduced order models (ROM). We use multi layer perceptrons (MLP) to learn a continuous in time closure model through the recently proposed Neural ODE method. Inspired by Taken's theorem as well as the Mori-Zwanzig formalism, we augment ROMs with a delay differential equation architecture to model non-Markovian effects in reduced models. The proposed model, called CD-ROM (Complementary Deep-Reduced Order Model) is able to retain information from past states of the system and use it to correct the imperfect reduced dynamics. The model can be integrated in time as a system of ordinary differential equations using any classical time marching scheme. We demonstrate the ability of our CD-ROM approach to improve the accuracy of POD-Galerkin models on two CFD examples, even in configurations unseen during training.