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For a number of years since its introduction to hydrology, recurrent neural networks like long short-term memory (LSTM) have proven remarkably difficult to surpass in terms of daily hydrograph metrics on known, comparable benchmarks.…

Computational fluid dynamics (CFD) simulations of complex fluid flows in energy systems are prohibitively expensive due to strong nonlinearities and multiscale-multiphysics interactions. In this work, we present a transformer-based modeling…

Machine learning offers an intriguing alternative to first-principles analysis for discovering new physics from experimental data. However, to date, purely data-driven methods have only proven successful in uncovering physical laws…

Model-free data-driven computational mechanics replaces phenomenological constitutive functions by numerical simulations based on data sets of representative samples in stress-strain space. The distance of strain and stress pairs from the…

Solving flow through porous media is a crucial step in the topology optimisation of cold plates, a key component in modern thermal management. Traditional computational fluid dynamics (CFD) methods, while accurate, are often prohibitively…

Because the Navier-Stokes equations are dissipative, the long-time dynamics of a flow in state space are expected to collapse onto a manifold whose dimension may be much lower than the dimension required for a resolved simulation. On this…

Multimodal data collected from the real world are often imperfect due to missing modalities. Therefore multimodal models that are robust against modal-incomplete data are highly preferred. Recently, Transformer models have shown great…

Non-Markovian dynamics are ubiquitous across physics, biology, and engineering. Yet our understanding of non-Markovian processes significantly lags that of simpler Markovian processes, due largely to a lack of tractable models. In this…

We introduce a data-driven approach to the modelling and analysis of viscous fluid mechanics. Instead of including constitutive laws for the fluid's viscosity in the mathematical model, we suggest to directly use experimental data. Only a…

In the manufacturing process, sensor data collected from equipment is crucial for building predictive models to manage processes and improve productivity. However, in the field, it is challenging to gather sufficient data to build robust…

Wall-bounded turbulent flows are chaotic and multiscale, rendering real-time prediction at high Reynolds numbers computationally prohibitive in applications such as wind farms. Classical data assimilation methods are based on repeated…

Traffic flow forecasting is essential and challenging to intelligent city management and public safety. Recent studies have shown the potential of convolution-free Transformer approach to extract the dynamic dependencies among complex…

Transformers predict over a representation of a sequence. The same data can be written as bytes, characters, or subword tokens, and these representations may be lossless. Yet, under a fixed context window, they need not expose the same…

There has been a recent surge of interest in time series modeling using the Transformer architecture. However, forecasting multivariate time series with Transformer presents a unique challenge as it requires modeling both temporal…

Thermodynamics with internal variables is a common approach in continuum mechanics to model inelastic (i.e., non-equilibrium) material behavior. While this approach is computationally and theoretically attractive, it currently lacks a…

A physics-informed convolutional neural network is proposed to simulate two phase flow in porous media with time-varying well controls. While most of PICNNs in existing literatures worked on parameter-to-state mapping, our proposed network…

Transformers are increasingly adopted for modeling and forecasting time-series, yet their internal mechanisms remain poorly understood from a dynamical systems perspective. In contrast to classical autoregressive and state-space models,…

We assess empirical models in climate econometrics using modern statistical learning techniques. Existing approaches are prone to outliers, ignore sample dependencies, and lack principled model selection. To address these issues, we…

High-dimensional dynamical systems projected onto a reduced-order model cease to be deterministic and are best described by probability distributions in state space. Their equations of motion map onto an evolution operator with a…

This paper introduces a novel data driven framework for constructing accurate and general equivariant models of multiscale phenomena which does not rely on specific assumptions about the underlying physics. This framework is illustrated…