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Over the past few years, we have seen fundamental breakthroughs in core problems in machine learning, largely driven by advances in deep neural networks. At the same time, the amount of data collected in a wide array of scientific domains…
Deep Learning research is advancing at a fantastic rate, and there is much to gain from transferring this knowledge to older fields like Computational Fluid Dynamics in practical engineering contexts. This work compares state-of-the-art…
Data taken from observations of the natural world or laboratory measurements often depend on parameters which can vary in unexpected ways. In this paper we demonstrate how machine learning can be leveraged to detect changes in global…
The Whitham equation is a nonlocal, nonlinear partial differential equation that models the temporal evolution of spatial profiles of surface displacement of water waves. However, many laboratory and field measurements record time series at…
Differential equation discovery, a machine learning subfield, is used to develop interpretable models, particularly in nature-related applications. By expertly incorporating the general parametric form of the equation of motion and…
The equations governing atmospheric flows are nonlinear. Consequently, the hierarchy of cumulant equations is not closed. But because atmospheric flows are inhomogeneous and anisotropic, the nonlinearity may manifest itself only weakly…
The understanding of sensor data has been greatly improved by advanced deep learning methods with big data. However, available sensor data in the real world are still limited, which is called the opportunistic sensor problem. This paper…
Machine learning techniques have been shown to be effective to recognize different phases of matter and produce phase diagrams in the parameter space interested, while they usually require prior labeled data to perform well. Here, we…
Marine heatwaves (MHWs), an extreme climate phenomenon, pose significant challenges to marine ecosystems and industries, with their frequency and intensity increasing due to climate change. This study introduces an integrated deep learning…
We present an implementation of an explainable and physics-aware machine learning model capable of inferring the underlying physics of high-energy particle collisions using the information encoded in the energy-momentum four-vectors of the…
The Ostrovsky--Hunter equation governs evolution of shallow water waves on a rotating fluid in the limit of small high-frequency dispersion. Sufficient conditions for the wave breaking in the Ostrovsky--Hunter equation are found both on an…
The low frequency variability of the extratropical atmosphere involves hemispheric-scale recurring, often persistent, states known as teleconnection patterns or regimes, which can have profound impact on predictability on intra-seasonal and…
Finding hidden layers in complex networks is an important and a non-trivial problem in modern science. We explore the framework of quantum graphs to determine whether concealed parts of a multi-layer system exist and if so then what is…
Breaking surface waves generate drops of a broad range of sizes that have a significant influence on regional and global climates, as well as the identification of ship movements. Characterizing these phenomena requires a fundamental…
In scientific machine learning, the task of identifying partial differential equations accurately from sparse and noisy data poses a significant challenge. Current sparse regression methods may identify inaccurate equations on sparse and…
We have studied the emergence of bound states in weakly deformed and/or heterogeneous waveguides, comparing the analytical predictions obtained using a recently developed perturbative method, with precise numerical results, for different…
With the recent success of representation learning methods, which includes deep learning as a special case, there has been considerable interest in developing techniques that incorporate known physical constraints into the learned…
The transition to turbulence in many shear flows proceeds along two competing routes, one linked with finite-amplitude disturbances and the other one originating from a linear instability, as in e.g. boundary layer flows. The dynamical…
Discovering the governing laws underpinning physical and chemical phenomena is a key step towards understanding and ultimately controlling systems in science and engineering. We introduce Discovery of Dynamical Systems via Moving Horizon…
The data-driven recovery of the unknown governing equations of dynamical systems has recently received an increasing interest. However, the identification of governing equations remains challenging when dealing with noisy and partial…