João Lucas de Sousa Almeida

Minh Triet Chau, João Lucas de Sousa Almeida, Elie Alhajjar et al.

A recent alternative for hydrogen transportation as a mixture with natural gas is blending it into natural gas pipelines. However, hydrogen embrittlement of material is a major concern for scientists and gas installation designers to avoid process failures. In this paper, we propose a physics-informed machine learning model to predict the gas pressure on the pipes' inner wall. Despite its high-fidelity results, the current PDE-based simulators are time- and computationally-demanding. Using simulation data, we train an ML model to predict the pressure on the pipelines' inner walls, which is a first step for pipeline system surveillance. We found that the physics-based method outperformed the purely data-driven method and satisfy the physical constraints of the gas flow system.

Imran Nasim, Joaõ Lucas de Sousa Almeida

Scientific Machine Learning is transforming traditional engineering industries by enhancing the efficiency of existing technologies and accelerating innovation, particularly in modeling chemical reactions. Despite recent advancements, the issue of solving stiff chemically reacting problems within computational fluid dynamics remains a significant issue. In this study we propose a novel approach utilizing a multi-layer-perceptron mixer architecture (MLP-Mixer) to model the time-series of stiff chemical kinetics. We evaluate this method using the ROBER system, a benchmark model in chemical kinetics, to compare its performance with traditional numerical techniques. This study provides insight into the industrial utility of the recently developed MLP-Mixer architecture to model chemical kinetics and provides motivation for such neural architecture to be used as a base for time-series foundation models.

João Lucas de Sousa Almeida, Arthur Cancellieri Pires, Klaus Feine Vaz Cid et al.

This work explores the physics-driven machine learning technique Operator Inference (OpInf) for predicting the state of chaotic dynamical systems. OpInf provides a non-intrusive approach to infer approximations of polynomial operators in reduced space without having access to the full order operators appearing in discretized models. Datasets for the physics systems are generated using conventional numerical solvers and then projected to a low-dimensional space via Principal Component Analysis (PCA). In latent space, a least-squares problem is set to fit a quadratic polynomial operator, which is subsequently employed in a time-integration scheme in order to produce extrapolations in the same space. Once solved, the inverse PCA operation is applied to reconstruct the extrapolations in the original space. The quality of the OpInf predictions is assessed via the Normalized Root Mean Squared Error (NRMSE) metric from which the Valid Prediction Time (VPT) is computed. Numerical experiments considering the chaotic systems Lorenz 96 and the Kuramoto-Sivashinsky equation show promising forecasting capabilities of the OpInf reduced order models with VPT ranges that outperform state-of-the-art machine learning methods such as backpropagation and reservoir computing recurrent neural networks [1], as well as Markov neural operators [2].

Imran Nasim, Joaõ Lucas de Sousa Almeida

The recently introduced class of architectures known as Neural Operators has emerged as highly versatile tools applicable to a wide range of tasks in the field of Scientific Machine Learning (SciML), including data representation and forecasting. In this study, we investigate the capabilities of Neural Implicit Flow (NIF), a recently developed mesh-agnostic neural operator, for representing the latent dynamics of canonical systems such as the Kuramoto-Sivashinsky (KS), forced Korteweg-de Vries (fKdV), and Sine-Gordon (SG) equations, as well as for extracting dynamically relevant information from them. Finally we assess the applicability of NIF as a dimensionality reduction algorithm and conduct a comparative analysis with another widely recognized family of neural operators, known as Deep Operator Networks (DeepONets).