Related papers: Gravitational Dimensionality Reduction Using Newto…
In this work, we investigate Riemannian geometry based dimensionality reduction methods that respect the underlying manifold structure of the data. In particular, we focus on Principal Geodesic Analysis (PGA) as a nonlinear generalization…
The recent classical nonlocal generalization of Einstein's theory of gravitation is presented within the framework of general relativity via the introduction of a preferred frame field. The nonlocal generalization of Einstein's field…
Modified General Relativity (MGR) is the natural extension of General Relativity (GR). MGR explicitly uses the smooth regular line element vector field $(\bm{X},-\bm{X}) $, which exists in all Lorentzian spacetimes, to construct a…
Recent work has shown deep learning can accelerate the prediction of physical dynamics relative to numerical solvers. However, limited physical accuracy and an inability to generalize under distributional shift limit its applicability to…
It is known that General Relativity ({\bf GR}) uses a Lorentzian Manifold $(M_4;g)$ as a geometrical model of the physical spacetime. The metric $g$ is required to satisfy Einstein's equations. Since the 1960s many authors have tried to…
The Doplicher, Fredenhagen and Roberts (DFR) noncommutative (NC) formalism is propose in a curved space-time. In DFR approach, the NC parameter is promoted to the set of coordinates of the space-time. As consequence, the field theory…
Gravitation, according to General Relativity, is an attribute of space-time's geometry and hence not a force in the Newtonian sense. This is a consequence of Einstein's equivalence principle, which so far passed all experimental tests with…
Scientific machine learning and the advent of the Physics-Informed Neural Network (PINN) have shown high potential in their ability to solve complex differential equations. One example is the use of PINNs to solve the gravity field modeling…
General Relativity (GR) describes gravitation well at the energy scales which we have so far been able to achieve or detect. However, we do not know whether GR is behind the physics governing stronger gravitational field regimes, such as…
With the advent of gravitational wave astronomy, techniques to extend the reach of gravitational wave detectors are desired. In addition to the stellar-mass black hole and neutron star mergers already detected, many more are below the…
In this talk, I present a theory of quantum gravity beyond Einstein. The theory is established based on spinnic and scaling gauge symmetries by treating the gravitational force on the same footing as the electroweak and strong forces. A…
General relativity differs from other forces in nature in that it can be made to disappear locally. This is the essence of the equivalence principle. In general relativity the equivalence principle is implemented using differential…
Analyzing relationships between objects is a pivotal problem within data science. In this context, Dimensionality reduction (DR) techniques are employed to generate smaller and more manageable data representations. This paper proposes a new…
We explore the new physics phenomena of gravidynamics governed by the inhomogeneous spin gauge symmetry based on the gravitational quantum field theory. Such a gravidynamics enables us to derive the generalized Einstein equation and an…
This work places the invariant $ds^2$ at the center of the gravitational interaction, interpreting it not as a purely geometric object but as the differential of proper time, endowed with direct physical meaning. Starting from the extension…
While Newtonian gravity is an adequate model for current geophysical exploration, Einsteinian gravity, based on the connection between free fall and warped time, has superseded Newtonian gravity as our best understanding of the universe.…
The presence of a massive body between the Earth and a gravitational-wave source will produce the so-called gravitational lensing effect. In the case of strong lensing, it leads to the observation of multiple deformed copies of the initial…
Guided by the Einstein equivalence principle that identifies the phenomenon of gravitation as a manifestation of the dynamics of spacetime in contrast to a localizable force, we review and explore its consequences on formulating a theory of…
Graph Neural Networks (GNNs) have gained popularity in various learning tasks, with successful applications in fields like molecular biology, transportation systems, and electrical grids. These fields naturally use graph data, benefiting…
The generalized $f(R)$ gravity with curvature-matter coupling in five-dimensional (5D) spacetime can be established by assuming a hypersurface-orthogonal spacelike Killing vector field of 5D spacetime, and it can be reduced to the 4D…