Imran Nasim

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.

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).

Imran Nasim, Melanie Weber

The problem of identifying geometric structure in data is a cornerstone of (unsupervised) learning. As a result, Geometric Representation Learning has been widely applied across scientific and engineering domains. In this work, we investigate the use of Geometric Representation Learning for the data-driven discovery of system dynamics from spatial-temporal data. We propose to encode similarity structure in such data in a spatial-temporal proximity graph, to which we apply a range of classical and deep learning-based manifold learning approaches to learn reduced order dynamics. We observe that while manifold learning is generally capable of recovering reduced order dynamics, the quality of the learned representations varies substantially across different algorithms and hyperparameter choices. This is indicative of high sensitivity to the inherent geometric assumptions of the respective approaches and suggests a need for careful hyperparameter tuning, which can be expensive in practise. To overcome these challenges, we propose a framework for Automated Manifold Learning, which selects a manifold learning approach and corresponding hyperparameter choices based on representative subsamples of the input graph. We demonstrate that the proposed framework leads to performance gains both in scalability and in the learned representations' accuracy in capturing local and global geometric features of the underlying system dynamics.