相关论文: Physically Constrained Covariance Inflation from L…
We introduce a physically relevant stochastic representation of the rotating shallow water equations. The derivation relies mainly on a stochastic transport principle and on a decomposition of the fluid flow into a large-scale component and…
Macroscopic traffic flow is stochastic, but the physics-informed deep learning methods currently used in transportation literature embed deterministic PDEs and produce point-valued outputs; the stochasticity of the governing dynamics plays…
Fourth-order accurate compact schemes for variable coefficient convection diffusion equations are considered. A sufficient condition for the stability of the fully discrete problem is derived using a difference equation based approach. The…
The possibility of thermally induced initial density perturbations in inflationary cosmology is examined. The fluctuation dynamics of a scalar field plus thermal bath system during slow roll is described by a Langevin-like equation.…
We consider problems in which a system receives external \emph{perturbations} from time to time. For instance, the system can be a train network in which particular lines are repeatedly disrupted without warning, having an effect on…
With present and future observations becoming of higher and higher quality, it is timely and necessary to investigate the most significant theoretical uncertainties in the predictions of inflation. We show that our ignorance of the entire…
Energy transport can be influenced by the presence of other conserved quantities. We consider here diffusive systems where energy and the other conserved quantities evolve macroscopically on the same diffusive space-time scale. In these…
It is shown that the squeezed limit of inflationary expectation values follows from reparametrization invariance of the wavefunction of the universe. This translates into a constraint on the longitudinal modes of functional derivatives of…
The stochastic approach aims at describing the long-wavelength part of quantum fields during inflation by a classical stochastic theory. It is usually formulated in terms of Langevin equations, giving rise to a Fokker-Planck equation for…
Most inverse problems from physical sciences are formulated as PDE-constrained optimization problems. This involves identifying unknown parameters in equations by optimizing the model to generate PDE solutions that closely match measured…
We analyze statistically the energization of particles in a large scale environment of strong turbulence that is fragmented into a large number of distributed current filaments. The turbulent environment is generated through strongly…
N-flation is a radiatively stable scenario for chaotic inflation in which the displacements of $N \gg 1$ axions with decay constants $f_1 \le \ldots \le f_N < M_P$ lead to a super-Planckian effective displacement equal to the Pythagorean…
We discuss a kinetically constrained model in which real-valued local densities fluctuate in time, as introduced recently by Bertin, Bouchaud and Lequeux. We show how the phenomenology of this model can be reproduced by an effective theory…
Scalar and tensor perturbations arising in an inflationary braneworld scenario driven by a single scalar field are considered, where the bulk on either side of the brane corresponds to Anti-de Sitter spaces with different cosmological…
The gradient expansion and the separate universe approach provide an effective description of inflationary soft modes after coarse-graining shorter-wavelength degrees of freedom. We formulate a locality condition on the quantum state,…
We apply the "systematic" $1^{st}$ order cosmological perturbation theory method to re-derive the formulation of an inflationary model generated by variation of constants, then to study the case where it is non-minimally coupled to gravity…
The perturbative approach to stochastic inflation is used to determine the spectrum of density fluctuations and gravitational waves due to the coarse grained field. The amplitude of the curvature fluctuation spectrum, the spectral index and…
We construct a model of inflation based on a low-energy effective theory of spontaneously broken global scale invariance. This provides a shift symmetry that protects the inflaton potential from quantum corrections. Since the underlying…
We study numerical algorithms to solve a specific Partial Differential Equation (PDE), namely the Stefan problem, using Physics Informed Neural Networks (PINNs). This problem describes the heat propagation in a liquid-solid phase change…
The forward problems of pattern formation have been greatly empowered by extensive theoretical studies and simulations, however, the inverse problem is less well understood. It remains unclear how accurately one can use images of pattern…