A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Paper shows how solutions to Allen-Cahn converge to multiphase mean curvature flow.
Proves existence of multiple solutions to a multiphasic equation on manifolds.
Unified framework for forward and inverse PDE problems in multiphase media.
The paper explores the geometric properties of fluid flows and their symmetries.
Study proves existence of expanding solutions for multiphase surfaces with regular junctions.
The Backlund transformation for pseudospherical surfaces, which is equivalent to that of the sine-Gordon equation, can be restricted to give a transformation on space curves that preserves constant torsion. We study its effects on closed curves (in particular, elastic rods) that generate multiphase solutions for the vo…
This paper proposes a deep neural network approach for predicting multiphase flow in heterogeneous domains with high computational efficiency. The deep neural network model is able to handle permeability heterogeneity in high dimensional systems, and can learn the interplay of viscous, gravity, and capillary forces fro…
We consider a Canham-Helfrich-type variational problem defined over closed surfaces enclosing a fixed volume and having fixed surface area. The problem models the shape of multiphase biomembranes. It consists of minimizing the sum of the Canham-Helfrich energy, in which the bending rigidities and spontaneous curvatures…
We address the minimization of the Canham-Helfrich functional in presence of multiple phases. The problem is inspired by the modelization of heterogeneous biological membranes, which may feature variable bending rigidities and spontaneous curvatures. With respect to previous contributions, no symmetry of the minimizers…
Framework automates microstructure image analysis for materials science.
Surrogate strategies are used widely for uncertainty quantification of groundwater models in order to improve computational efficiency. However, their application to dynamic multiphase flow problems is hindered by the curse of dimensionality, the saturation discontinuity due to capillarity effects, and the time-depende…
Paper proposes hybrid machine learning for tuning first principles models in engineering systems.
Jointly estimates flow fields and particle properties from Lagrangian data.
We present a general definition of the Poisson bracket between differential forms on the extended multiphase space appearing in the geometric formulation of first order classical field theories and, more generally, on exact multisymplectic manifolds. It is well defined for a certain class of differential forms that we …
SURGIN uses generative models to infer subsurface flow data efficiently.
We study the stability of partitions involving two or more phases in convex domains under the assumption of at most two-phase contact, thus excluding in particular triple junctions. We present a detailed derivation of the second variation formula with particular attention to the boundary terms, and then study the sign …
Reduces observables on multisymplectic manifolds using Lie algebra actions.
Medical image registration is one of the key processing steps for biomedical image analysis such as cancer diagnosis. Recently, deep learning based supervised and unsupervised image registration methods have been extensively studied due to its excellent performance in spite of ultra-fast computational time compared to …
This essay examines how what is considered to be artificial intelligence (AI) has changed over time and come to intersect with the expertise of the author. Initially, AI developed on a separate trajectory, both topically and institutionally, from pattern recognition, neural information processing, decision and control …
This paper presents a generalization of symplectic geometry to a principal bundle over the configuration space of a classical field. This bundle, the vertically adapted linear frame bundle, is obtained by breaking the symmetry of the full linear frame bundle of the field configuration space, and it inherits a generaliz…
We present a novel technique for assessing the dynamics of multiphase fluid flow in the oil reservoir. We demonstrate an efficient workflow for handling the 3D reservoir simulation data in a way which is orders of magnitude faster than the conventional routine. The workflow (we call it "Metamodel") is based on a projec…
This paper presents generalized momentum mappings for covariant Hamiltonian field theories. The new momentum mappings arise from a generalization of symplectic geometry to , the bundle of vertically adapted linear frames over the bundle of field configurations . Specifically, the generalized field momentum obs…
Framework learns physics-informed continuum models from molecular data.
Modeling 3D continua with singular points using Yin sets.
Microstructures of a material form the bridge linking processing conditions - which can be controlled, to the material property - which is the primary interest in engineering applications. Thus a critical task in material design is establishing the processing-structure relationship, which requires domain expertise and …
How to give a natural geometric definition of a covariant Poisson bracket in classical field theory has for a long time been an open problem - as testified by the extensive literature on "multisymplectic Poisson brackets", together with the fact that all these proposals suffer from serious defects. On the other hand, t…
In this paper a data analytical approach featuring support vector machines (SVM) is employed to train a predictive model over an experimentaldataset, which consists of the most relevant studies for two-phase flow pattern prediction. The database for this study consists of flow patterns or flow regimes in gas-liquid two…
This research examines how the error rate of nearest neighbor classifiers varies with dataset size.
Experimental design is crucial for inference where limitations in the data collection procedure are present due to cost or other restrictions. Optimal experimental designs determine parameters that in some appropriate sense make the data the most informative possible. In a Bayesian setting this is translated to updatin…
In coronary CT angiography, a series of CT images are taken at different levels of radiation dose during the examination. Although this reduces the total radiation dose, the image quality during the low-dose phases is significantly degraded. To address this problem, here we propose a novel semi-supervised learning tech…
Neurons predict future scalar inputs by learning top modes of lag vectors.
This is the second in a series of papers discussing in the framework of gerbe theory canonical and geometric aspects of the 2d nonlinear sigma model in the presence of conformal defects in the worldsheet. Employing the formal tools worked out in the first paper of the series, 1101.1126 [hep-th], a thorough analysis of …
Study Galois groupoids of discret Painlevé equations.
Proves solvability of general inverse σ_k equations with constant coefficients.
We present an unsupervised approach for discovering semantic representations of mathematical equations. Equations are challenging to analyze because each is unique, or nearly unique. Our method, which we call equation embeddings, finds good representations of equations by using the representations of their surrounding …
Paper establishes estimates for nonlinear equations on compact manifolds.
Proves C^2,alpha estimates for elliptic equations on hyperkähler manifolds.
The paper generalizes Monge-Ampère equations and their solutions in differential geometry.
We study four distinct second-order nonlinear equations of Rabelo which describe pseudospherical surfaces. By transforming these equations to the constant-characteristic form we relate them to some well-studied integrable equations. Two of the Rabelo equations are found to be related to the sine-Gordon equation. The ot…
Introduces a new PDE involving differential forms for Kähler geometry.
Sharp sub-Gaussian bounds for subsolutions of Trudinger's equation on Riemannian manifolds.
In this paper we perform a blow-up and quantization analysis of the following nonlocal Liouville-type equation \begin{equation}(-Δ)^\frac12 u= κe^u-1~\mbox{in ,} \end{equation} where stands for the fractional Laplacian and is a bounded function. We interpret the above equation as the prescri…
The paper derives gradient estimates for porous medium and fast diffusion equations on metric measure spaces.
Paper solves Hessian equations on Kähler manifolds.
The paper introduces new equations in Kähler geometry and proves their solutions and convexity.
We describe a method to reduce partial differential equations of Monge-Ampère type in 4 variables to complex partial differential equations in 2 variables. To illustrate this method, we construct explicit holomorphic solutions of the special lagrangian equation, the real Monge-Ampère equations and the Plebanski equatio…
Probabilistic grammars improve equation discovery from data.
In this paper, we provide families of second order non-linear partial differential equations, describing pseudospherical surfaces (pss equations), with the property of having local isometric immersions in E^3, with principal curvatures depending on finite-order jets of solutions of the differential equation. These equa…