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Magnetic fields play an important role in many astrophysical systems and a detailed understanding of their impact on the gas dynamics requires robust numerical simulations. Here we present a new method to evolve the ideal…
We propose Geometric Pareto Control (GPC), a framework overcoming barriers of reinforcement learning in cyber-physical systems where governing physics is known. Reinforcement learning confronts barriers in safety-critical applications:…
Group equivariant neural networks are used as building blocks of group invariant neural networks, which have been shown to improve generalisation performance and data efficiency through principled parameter sharing. Such works have mostly…
Graph transformers achieve strong results on molecular and long-range reasoning tasks, yet remain hampered by over-smoothing (the progressive collapse of node representations with depth) and attention entropy degeneration. We observe that…
We derive new models of stochastic Hall magnetohydrodynamics (MHD) by using a symmetry-reduced stochastic Euler-Poincar\'e variational principle. The new stochastic Hall MHD theory has potential applications for uncertainty quantification…
Estimating the depths of equirectangular (i.e., 360) images (EIs) is challenging given the distorted 180 x 360 field-of-view, which is hard to be addressed via convolutional neural network (CNN). Although a transformer with global attention…
We propose a novel approach for performing convolution of signals on curved surfaces and show its utility in a variety of geometric deep learning applications. Key to our construction is the notion of directional functions defined on the…
We introduce Steerable Transformers, an extension of the Vision Transformer mechanism that maintains equivariance to the special Euclidean group $\mathrm{SE}(d)$. We propose an equivariant attention mechanism that operates on features…
Hybrid beamformer design plays very crucial role in the next generation millimeter-wave (mm-Wave) massive MIMO (multiple-input multiple-output) systems. Previous works assume the perfect channel state information (CSI) which results heavy…
We present a novel data-driven approach for enhancing gradient reconstruction in unstructured finite volume methods for hyperbolic conservation laws, specifically for the 2D Euler equations. Our approach extends previous structured-grid…
To bridge the gap between empirical success and theoretical understanding in transfer reinforcement learning (RL), we study a principled approach with provable performance guarantees. We introduce a novel composite MDP framework where…
Euclidean geometry has historically been the typical "workhorse" for machine learning applications due to its power and simplicity. However, it has recently been shown that geometric spaces with constant non-zero curvature improve…
The Transformer architecture has recently gained considerable attention in the field of graph representation learning, as it naturally overcomes several limitations of Graph Neural Networks (GNNs) with customized attention mechanisms or…
Magnetohydrodynamics (MHD) couples the Navier--Stokes and Maxwell equations into a nonlinear system of partial differential equations governing stellar interiors, astrophysical jets, fusion plasmas, and space weather. Numerical advances,…
Kinodynamic planning for car-like vehicles on uneven terrain requires simultaneously optimizing competing objectives such as path efficiency and pose stability. This work presents an adaptive epsilon-constraint method integrated into a…
An exotic rotationally invariant harmonic oscillator (ERIHO) is constructed by applying a non-unitary isotropic conformal bridge transformation (CBT) to a free planar particle. It is described by the isotropic harmonic oscillator…
This paper provides a further step in our program of studying superconformal nets over S^1 from the point of view of noncommutative geometry. For any such net A and any family Delta of localized endomorphisms of the even part A^gamma of A,…
We develop a unified geometric framework for mechanical systems that combine conservative and dissipative dynamics by formulating them on contact manifolds. Within this setting, we identify the Reeb vector field as the intrinsic generator…
High-performance multimode/multiwavelength (de)multiplexer is one of the most pivotal photonic devices for advanced on-chip interconnect systems. Traditional on-chip photonic (de)multiplexing requires large device footprint for maintaining…
This paper presents a framework for analyzing and designing cylindrical omega-bianisotropic metasurfaces, inspired by mode matching and digital signal processing techniques. Using the discrete Fourier transform, we decompose the the…