Method generates joint posterior samples of source and foreground mass distributions for gravitational lensing.
problem Challenging inference problem for high-resolution, high signal-to-noise ratio gravitational lensing.
method Combines diffusion-based generative modeling and recurrent inference machines.
result Can model realistic gravitational lensing simulations down to the noise level.
Estimates how many times a star appears due to gravitational lensing.
problem Estimating the number of times an observer sees a star due to gravitational lensing.
method Use affine linking numbers to estimate the number of times an observer sees a star.
result Estimates the number of times an observer sees a star due to gravitational lensing.
Deep learning helps remove secondary B-mode polarization to detect primordial gravitational waves.
problem Removing secondary B-mode polarization from CMB data to detect primordial gravitational waves. method Applied deep learning (ResUNet-CMB) to estimate and remove multiple sources of secondary B-mode polarization. result Deep learning can produce nearly optimal, unbiased estimates of the amplitude of primordial gravitational waves.
Paper uses ResUNet-CMB to reconstruct cosmic polarization rotation from CMB data.
problem Reconstructing anisotropic cosmic polarization rotation from CMB data.
method Extended ResUNet-CMB to handle gravitational lensing and patchy reionization.
result ResUNet-CMB outperforms standard quadratic estimator in reconstructing all three effects.
Next-generation cosmic microwave background (CMB) experiments will have lower noise and therefore increased sensitivity, enabling improved constraints on fundamental physics parameters such as the sum of neutrino masses and the tensor-to-scalar ratio r. Achieving competitive constraints on these parameters requires hig…
ResUNet-CMB neural network reconstructs CMB effects from noisy data.
problem Reconstructing CMB anisotropies from noisy data.
method Convolutional neural network (ResUNet-CMB) for simultaneous reconstruction of lensing and reionization.
result ResUNet-CMB outperforms quadratic estimators at low noise levels and avoids lensing-induced bias.
We provide a geometric explanation for the existence of magnification relations for the A, D, E family of caustic singularities, which were established in recent work. In particular, it was shown that for families of general mappings between planes exhibiting any of these caustic singularities, and for any non-caustic …
Enhances weak lensing inference with neural summaries.
problem Extracting additional information from weak lensing convergence maps.
method Hybrid approach combining physics-based and neural summaries.
result Neural summaries extract up to 8 times more information than angular power spectra.
In the Friedmann Model of the universe, cosmologists assume that spacelike slices of the universe are Riemannian manifolds of constant sectional curvature. This assumption is justified via Schur's Theorem by stating that the spacelike universe is locally isotropic. Here we define a Riemannian manifold as almost locally…
We pursue a geometrical approach to gravitational lensing theory. We present a survey of the background theory of General Relativity, including particular properties of the Schwarzschild and Kerr solutions. Next we outline a proof of the Gauss Bonnet theorem and its applications to surfaces in optical geometry, as deve…
Machine learning detects subhalos in lensed images with high accuracy and low false positives.
problem Detecting substructure in strongly lensed images.
method Developed a neural network for image segmentation to locate and mass estimate subhalos.
result The network can detect subhalos with masses m≳108.5M⊙ and measure the subhalo mass function. First we review the definition of a negative point mass singularity. Then we examine the gravitational lensing effects of these singularities in isolation and with shear and convergence from continuous matter. We review the Inverse Mean Curvature Flow and use this flow to prove some new results about the mass of a sing…
In general relativity, spatial light rays of static spherically symmetric spacetimes are geodesics of surfaces in Riemannian optical geometry. In this paper, we apply results on the isoperimetric problem to show that length-minimizing curves subject to an area constraint are circles, and discuss implications for the ph…
Evidence Networks simplify Bayesian model comparison for complex models.
problem Bayesian model comparison challenges with intractable likelihoods or priors.
method Loss functions and neural networks for fast, amortized estimation of Bayes factors.
result Evidence Networks provide accurate and scalable Bayes factor estimation.
TopoFisher learns topological summaries by maximizing Fisher information, improving parameter efficiency and inference quality.
problem Simulation-based inference misses key information in low-order statistics, especially for non-Gaussian fields.
method TopoFisher uses a differentiable persistent-homology pipeline that learns topological summaries by maximizing local Gaussian Fisher information.
result TopoFisher recovers much of the available information and outperforms fixed topological vectorizations in weak gravitational lensing.
Weak lensing maps contain information beyond two-point statistics on small scales. Much recent work has tried to extract this information through a range of different observables or via nonlinear transformations of the lensing field. Here we train and apply a 2D convolutional neural network to simulated noiseless lensi…
New model reduces bias in cosmic shear measurements.
problem Bias in cosmic shear measurements due to non-well-defined ellipticity.
method Hybrid physical and deep learning Hierarchical Bayesian Model.
result Unbiased estimate of shear on realistic galaxies.
The subtle and unique imprint of dark matter substructure on extended arcs in strong lensing systems contains a wealth of information about the properties and distribution of dark matter on small scales and, consequently, about the underlying particle physics. However, teasing out this effect poses a significant challe…
New black hole solutions with lens space horizons in 5D Kaluza-Klein theory.
problem Finding black hole solutions with specific horizon topologies.
method Formally asymptotically flat black hole solutions constructed through Kaluza-Klein reduction.
result Explicit construction of regular black hole solutions with L(p,q) horizons. New equations reveal how cylinder power in progressive lenses depends on geodesic curvature.
problem Current understanding of cylinder power in progressive lenses is incomplete.
method Derived complete compatibility equations for spatially-varying curvature surfaces.
result Cylinder power depends on geodesic curvature, not just principal curvature.
Framework synthesizes programs for simulating complex models and estimating parameters.
problem Parameter estimation for complex models requires manual encoding of fixed model structures.
method Combines LLMs for program synthesis with neural simulation-based inference.
result Identifies plausible model families from open-ended prompts with high accuracy.
Deep learning reduces noise in weak lensing mass maps using GANs.
problem Noise reduction in weak lensing mass maps.
method Generative adversarial networks (GANs) applied to Subaru Hyper Suprime-Cam data.
result GANs successfully reproduce non-Gaussian information in denoised maps, showing stronger cosmological dependence.
Dynamic SBI improves SBI efficiency without rounds, reducing simulation and training costs.
problem Efficiently perform complex scientific inference with high-dimensional data.
method Adaptive dataset transformation, parallel simulation and training.
result Significant improvements in simulation and training efficiency.
We demonstrate the potential of Deep Learning methods for measurements of cosmological parameters from density fields, focusing on the extraction of non-Gaussian information. We consider weak lensing mass maps as our dataset. We aim for our method to be able to distinguish between five models, which were chosen to lie …
The modulation transfer function (MTF) is widely used to characterise the performance of optical systems. Measuring it is costly and it is thus rarely available for a given lens specimen. Instead, MTFs based on simulations or, at best, MTFs measured on other specimens of the same lens are used. Fortunately, images reco…
Classifies gravitational instantons with quadratic volume growth.
problem Classifying gravitational instantons with specific growth properties.
method Proves a classification theorem for ALG∗ gravitational instantons, determines topology, and proves existence of uniform coordinates. result Proves a relationship between ALG gravitational instantons of different orders.
Survey of recent progress in gravitational instantons
problem Classification of hyperkähler and Hermitian gravitational instantons
method Survey of recent progress in gravitational instantons
result Survey of recent progress in gravitational instantons
New emulator bridges simulators using conditional optimal transport.
problem Bridging simulators with minimal distortion.
method Flow-based approach to learn likelihood transport, COT-FM for optimal matching.
result Emulator accurately captures full correction between simulators.
The paper proves unique characterization of gravitational instantons with specific volume growth.
problem Characterizing gravitational instantons with quadratic volume growth.
method Defining a period mapping and proving its surjectivity and openness.
result The periods uniquely characterize ALG∗ and ALG gravitational instantons up to diffeomorphism. Period maps surjective for certain gravitational instantons.
problem Understanding the uniformization of gravitational instantons.
method Uniformization theorems by Chen--Chen, Chen--Viaclovsky, Collins--Jacob--Lin, and Hein--Sun--Viaclovsky--Zhang.
result Period maps surjective for ALH*, ALG, and ALG* gravitational instantons.
Authors prove Torelli theorem for a specific type of gravitational instantons.
problem Identifying diffeomorphism types of gravitational instantons.
method Using mirror special Lagrangian fibrations and recent work on rational elliptic surfaces.
result Identify 10 diffeomorphism types of ALHb∗ gravitational instantons. This is our third paper in a series on the gravitational instantons. In this paper, we classify ALG and ALH gravitational instantons. In ALG case, we extend Hein's construction slightly and show that it's the only ALG gravitational instanton. In ALH case, we prove a Torelli-type theorem.
Gravitational instantons are non-Kähler, providing a counterexample to Euclidean Black Hole Uniqueness.
problem Classical Euclidean Black Hole Uniqueness conjecture
method Analyzing the Chen-Teo gravitational instanton
result The Chen-Teo instanton is Hermitian and non-Kähler
Existence proved for specific types of gravitational instantons.
problem Existence of toric ALE and ALF gravitational instantons.
method Established existence and uniqueness results for ALE and ALF gravitational instantons.
result Existence of a unique, Ricci-flat, toric ALE and ALF gravitational instanton for every admissible rod structure.
This is our second paper in a series to study gravitational instantons, i.e. complete hyperkäler 4-manifolds with faster than quadratic curvature decay. We prove two main theorems: 1.The asymptotic rate of gravitational instantons to the standard models can be improved automatically. 2.Any ALF-D_k gravitational instant…
New gravitational energy measure $\Q$ found in higher dimensions.
problem Characterizing local gravitational energy in higher dimensions.
method Study of quasilocal mass proposals in higher dimensions.
result New quantity $\Q$ replaces Bel-Robinson superenergy Q in vacuum limits. The holographic description in the presence of gravitational Chern-Simons term is studied. The modified gravitational equations are integrated by using the Fefferman-Graham expansion and the holographic stress-energy tensor is identified. The stress-energy tensor has both conformal anomaly and gravitational or, if re-f…
Proves infinitesimal rigidity of Hermitian gravitational instantons.
problem Understanding the moduli space of Hermitian gravitational instantons.
method Proof of infinitesimal rigidity and integrability using boundary conditions and conformal Kähler properties.
result Completes the understanding of Hermitian gravitational instantons, both compact and non-compact.
Study proves interaction of three impulsive gravitational waves, showing local solution and Lipschitz continuity.
problem Interaction of three impulsive gravitational waves in Einstein vacuum equations.
method Geometric estimates and wave estimates to prove local solution and continuity.
result Local solution to Einstein vacuum equations with three impulsive gravitational waves, Lipschitz continuity.
New approach proves existence of gravitating vortices on Riemann surfaces.
problem Existence of gravitating vortices on Riemann surfaces.
method Symplectic reduction by stages and reduced α-K-energy. result Existence of solutions implies polystability of effective divisors.
Review of gravitational instantons in physics.
problem Understanding solutions to Einstein equations in four dimensions.
method Lecture review of examples.
result Examples of gravitational instantons.
Gravitational instantons collapse to a punctured plane with a special Kahler metric.
problem The collapse of gravitational instantons from a complex structure limit.
method Analysis of a sequence of ALH*-gravitational instantons and their collapse to a punctured plane.
result The moduli space of pointed ALH*-gravitational instantons collapses to a punctured plane with a special Kahler metric.
The holographic duality can be extended to include quantum theories with broken coordinate invariance leading to the appearance of the gravitational anomalies. On the gravity side one adds the gravitational Chern-Simons term to the bulk action which gauge invariance is only up to the boundary terms. We analyze in detai…
Researchers embed gravitational instantons in higher-dimensional spaces.
problem Embedding gravitational instantons in higher-dimensional spaces.
method Construct isometric and conformally isometric embeddings of gravitational instantons in R8 and R7. result Embedding class of the Einstein--Maxwell instanton is equal to 3.
Gravitational waves are predicted by the general theory of relativity. In [6] D. Christodoulou showed that gravitational waves have a nonlinear memory. We proved in [3] that the electromagnetic field contributes at highest order to the nonlinear memory effect of gravitational waves. In the present paper, we study this …
Charge measurements for instantons and gravitational perturbations.
problem Evaluating charges in Hermitian non-Kähler Einstein 4-manifolds and their perturbations.
method Evaluation of charges via Killing spinors and perturbation analysis of gravitational instantons.
result Generic gravitational perturbations admit a closed 2-form measuring the charge change.
In this paper we explicitly calculate the analogue of the 't Hooft SU(2) Yang--Mills instantons on Gibbons--Hawking multi-centered gravitational instantons which come in two parallel families: the multi-Eguchi--Hanson, or A_k ALE gravitational instantons and the multi-Taub--NUT, or A_k ALF gravitational instantons. We …
Study of twistor spaces and minitwistor spaces for ALE gravitational instantons.
problem Characterizing the geometry of ALE gravitational instantons of type Amodd. method Analyzing the base locus of linear systems and using distinguished twistor lines.
result Explicit determination of images of certain twistor lines and description of real minitwistor lines.