clifford resnet
STAResNet: a Network in Spacetime Algebra to solve Maxwell's PDEs
Pepe, Alberto, Buchholz, Sven, Lasenby, Joan
Geometric Algebra Networks, also known as Clifford Algebra Networks, leverage the mathematical framework of Geometric Algebra to represent and manipulate data. Geometric Algebra is a powerful, high-dimensional algebraic system that extends traditional linear algebra, enabling the compact and intuitive representation of geometric transformations, rotations, and reflections [2, 3, 4]. In GA networks, data and operations are expressed in terms of multivectors, which can capture complex geometric relationships more naturally than traditional tensor or matrix representations. Early proposals for neural networks working in Geometric Algebra (GA) can be found in the literature from the end of the last century [5, 6, 7]. However, it is only in the past few years that the need for an effective and intuitive approach to geometrical problems in learning has sparked renewed interest in the field. Today, several architectures in GA exist, capable of handling convolutions and Fourier transforms [1, 8], performing rotations and rigid body motions [9, 10], and preserving end-to-end equivariance [11, 12, 13]. In recent years, the use of machine learning, particularly neural networks, to solve partial differential equations (PDEs) has gained significant traction [14, 15, 16, 17]. State-of-the-art approaches include physics-informed neural networks (PINNs) [18, 19, 20], Fourier neural operators [21, 22], and deep Ritz methods [23, 24].
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