New BdryMatérn GP model for reliable boundary integration on irregular domains.
problem Incorporating boundary information in Gaussian process models for complex phenomena.
method Proposes a novel BdryMatérn GP framework with a new covariance kernel derived via path integral and stochastic PDE.
result Sample paths from the BdryMatérn GP satisfy desired boundaries with smoothness control on derivatives.
LLapDiff models irregular multivariate time series without step-by-step integration.
problem Trade-off between discrete and continuous methods for long-horizon forecasting.
method Generative framework that models target as a low-dimensional latent trajectory, guided by modal parameterization and Laplace domain poles.
result Improves long-horizon forecasting over baselines and supports missing-value imputation.
DAFNO learns surrogates for complex systems on irregular geometries.
problem Learning accurate surrogates for complex physical systems on irregular geometries.
method DAFNO incorporates a smoothed characteristic function in the integral layer architecture of FNOs, leveraging FFT for rapid computations.
result DAFNO achieves state-of-the-art accuracy on material modeling and airfoil simulation datasets.
daep learns from irregular, multimodal astronomical data.
problem Learning from irregular, multimodal astronomical sequences.
method Diffusion Autoencoder with Perceivers (daep) tokenizes, compresses, and reconstructs data.
result daep outperforms VAE and maep baselines in reconstruction and fine-scale structure preservation.
Most transport theorems---that is, a formula for the rate of change of an integral in which both the integrand and domain of integration depend on time---involve domains that evolve according to a flow map. Such domains are said to be convecting. Here a transport theorem for nonconvecting domains evolving on an embedde…
Machine learning methods such as convolutional neural networks (CNNs) are becoming an integral part of scientific research in many disciplines, spatial vector data often fail to be analyzed using these powerful learning methods because of its irregularities. With the aid of graph Fourier transform and convolution theor…
New method forecasts values and timing in irregular time series.
problem Forecasting values and timing in sparse, irregularly sampled multivariate time series.
method Proposes a novel approach for forecasting values and timing in irregular time series.
result Successfully forecasts values and timing in irregular time series.
DET unifies geometric and functional alignment for high-dimensional scientific data.
problem Challenges in nonrigid registration for high-dimensional, irregular data.
method Domain Elastic Transform (DET) treats data as functions on irregular domains, using a Bayesian framework for elastic motion registration.
result DET achieves 92% topological preservation on MERFISH data and successfully registers whole-embryo Stereo-seq atlases.
We present a novel and hierarchical approach for supervised classification of signals spanning over a fixed graph, reflecting shared properties of the dataset. To this end, we introduce a Convolutional Cluster Pooling layer exploiting a multi-scale clustering in order to highlight, at different resolutions, locally con…
Transformer-based multi-scale model outperforms traditional methods in solving PDEs on irregular domains.
problem Solving partial differential equations on irregular domains using deep learning.
method Introduces Multi-Scale Attention Transformer (\msat{}) for solving PDEs.
result Achieves state-of-the-art generalization on complex geometry problems with significant speedup.
TK-GCN forecasts spatiotemporal dynamics using Koopman-enhanced graph convolutional networks.
problem Forecasting complex spatiotemporal dynamics over irregular domains.
method Two-stage framework: Koopman-enhanced Graph Convolutional Network (K-GCN) for spatial encoding and Transformer for temporal modeling.
result TK-GCN outperforms state-of-the-art methods in spatiotemporal cardiac dynamics forecasting.
Efficient surrogate modeling for complex PDEs with physical laws.
problem High computational cost of repeated PDE simulations.
method LC-prior Gaussian process with POD and RBF-FD.
result Significantly reduced computational cost and improved accuracy.
We study in detail Hodge-Helmholtz decompositions in non-smooth exterior domains filled with inhomogeneous and anisotropic media. We show decompositions of alternating differential forms belonging to weighted Sobolev spaces into irrotational and solenoidal forms. These decompositions are essential tools, for example, i…
The paper introduces surface signatures for irregular surfaces and rough surfaces.
problem Characterizing and integrating highly irregular paths and surfaces.
method Introducing surface signatures and proving extension theorems.
result Surface signatures are universal for surface holonomy and rough surfaces.
GRUwE improves irregular time series prediction with simpler, efficient RNN-based approach.
problem Irregularly sampled multivariate time series prediction challenges.
method Gated Recurrent Unit with Exponential basis functions (GRUwE).
result GRUwE achieves competitive or superior performance compared to recent state-of-the-art methods.
The understanding of geographical reality is a process of data representation and pattern discovery. Former studies mainly adopted continuous-field models to represent spatial variables and to investigate the underlying spatial continuity/heterogeneity in the regular spatial domain. In this article, we introduce a more…
Proposes LSGP for better graph signal representation.
problem Local variations in graph process characteristics.
method Locally stationary graph process (LSGP) model.
result LSGP provides accurate signal representations.
Study on flat connections with controlled irregularity.
problem Boundedness of algebraic flat connections with limited irregularity.
method Analysis of families of algebraic flat connections and holonomic D-modules.
result Established boundedness of families of algebraic flat connections with controlled irregularity.
Neural Jump ODEs improve online filtering and classification with robust performance.
problem Online filtering and classification in settings with irregular and partial observations.
method Modeling conditional expectation using Neural Jump ODEs, with theoretical convergence guarantees.
result Demonstrated superior performance over classical methods, especially in complex scenarios.
To detect the irregular trade behaviors in the stock market is the important problem in machine learning field. These irregular trade behaviors are obviously illegal. To detect these irregular trade behaviors in the stock market, data scientists normally employ the supervised learning techniques. In this paper, we empl…
EDICT learns evidential distributions for irregular time series, improving predictions and uncertainty quantification.
problem Challenges in predicting and characterizing uncertainty for irregular time series data.
method EDICT (Evidential Distributions for Irregular Time Series) learns a continuous-time evidential distribution.
result EDICT achieves competitive performance on time series classification tasks and provides better uncertainty quantification.
With the developments of the last decade on complete constant mean curvature 1 (CMC 1) surfaces in the hyperbolic 3-space H3, many examples of such surfaces are now known. However, most of the known examples have regular ends. (An end is irregular, resp. regular, if the hyperbolic Gauss map of the surface has an ess…
We show that there are no irregular Sasaki-Einstein structures on rational homology 5-spheres. On the other hand, using K-stability we prove the existence of continuous families of non-toric irregular Sasaki-Einstein structures on odd connected sums of S2×S3.
The paper studies complex affine structures near irregular singularities.
problem Understanding complex affine structures near irregular singularities.
method Introducing local invariants and a Delaunay decomposition.
result Upper bounds on the complexity of the Delaunay decomposition.
Study deformation spaces of irregular isomonodromy systems on Riemann surfaces.
problem Understanding the topology of irregular isomonodromy systems.
method Define and study moduli spaces of deformations of irregular classes on Riemann surfaces.
result Generalize G-braid groups to study fundamental groups of deformation spaces.
We propose a class of intrinsic Gaussian processes (in-GPs) for interpolation, regression and classification on manifolds with a primary focus on complex constrained domains or irregular shaped spaces arising as subsets or submanifolds of R, R2, R3 and beyond. For example, in-GPs can accommodate spatial domains arising…
SDIFT generates full-field dynamics from sparse, irregular data.
problem Modeling and reconstructing physical dynamics from sparse, off-grid observations.
method SDIFT uses a functional Tucker model and sequential diffusion for generating full-field evolution from irregular sparse observations.
result Significant improvements in reconstruction accuracy and computational efficiency compared to state-of-the-art approaches.
We construct a new five parameter family of constant mean curvature trinoids with two asymptotically Delaunay ends and one irregular end.
TimeAutoML learns effective representations for irregularly sampled MTS data without manual tuning.
problem Learning effective representations for multivariate time series with irregular sampling rates and variable lengths.
method Autonomous representation learning pipeline with negative sample generation and auxiliary classification task.
result TimeAutoML achieves up to 20% performance improvement in anomaly detection on UCR datasets.
CRUs model irregular time series with continuous hidden states.
problem Handling irregular time intervals in sequential data.
method Continuous Recurrent Units (CRUs) that integrate hidden states via a linear stochastic differential equation.
result CRUs outperform methods based on neural ordinary differential equations in irregular time series interpolation.
For a complex polynomial in two variables we study the morphism induced in homology by the embedding of an irregular fiber in a regular neighborhood of it. We give necessary and sufficient conditions for this morphism to be injective, surjective. Particularly this morphism is an isomorphism if and only if the correspon…
The book is devoted to study so-called irregular subsets of the Grassmannian manifold Gkn(V) (this class of sets was introduced by author). In the previous variant of the book we restrict ourself only to the case when V is an n-dimensional vector space under the field R. Now we consider irregular subsets …
ACSSM models irregular time series with continuous dynamics.
problem Modeling irregular time series data.
method ACSSM uses a multi-marginal Doob's h-transform and variational inference with stochastic optimal control.
result ACSSM outperforms in tasks like classification, regression, interpolation, and extrapolation.
Neural Laplace Control tackles offline RL for continuous-time delayed systems with irregular observations.
problem Offline reinforcement learning problems involving continuous-time environments with delays and irregular observations.
method Combines a Neural Laplace dynamics model with a model predictive control (MPC) planner.
result Achieves near expert policy performance on continuous-time delayed environments.
Study on how sampling works for complex data functions.
problem Analyzing convergence of sampling algorithms for RKHS functions.
method Minimalistic assumptions on kernel and data, error estimates in RKHS norm, uniform convergence on compact domains.
result New convergence rates for Lipschitz and Hölder continuous kernels.
In-BO optimizes complex constrained domains using SIn-GP surrogate models.
problem Optimizing in complex constrained domains with irregular shapes.
method Sparse Intrinsic Gaussian Processes (SIn-GP) on manifolds with heat kernel estimation.
result In-BO outperforms traditional BO in complex constrained domains.
Study local wild mapping class groups for irregular connections on complex curves.
problem Understanding the moduli spaces of irregular connections on complex curves.
method Using isomonodromic deformations, focusing on reflections cosets, and introducing fission trees.
result Complete classification of local wild mapping class groups for various structure groups.
Survey on learning models for irregularly sampled time series data.
problem Challenges in learning from non-uniformly sampled time series data.
method Survey of recent models and architectures based on temporal discretization, interpolation, recurrence, attention, and structural invariance.
result Significant progress in machine learning for irregularly sampled time series data.
Improved MCMC sampling for expensive, irregular likelihoods.
problem Bayesian inference challenges with irregular, expensive likelihoods.
method Adapt subset samplers, introduce data-driven proxies, adaptive controller.
result Improved HINTS algorithm achieves best sampling error in fixed budget.
We study topological recursion on the irregular spectral curve xy2−xy+1=0, which produces a weighted count of dessins d'enfant. This analysis is then applied to topological recursion on the spectral curve xy2=1, which takes the place of the Airy curve x=y2 to describe asymptotic behaviour of enumerative proble…
Paper develops a method for causal representation learning from irregular tensors.
problem Complex patterns in high-dimensional, irregular tensor data.
method Novel causal formulation and CaRTeD framework integrating temporal causal representation learning with irregular tensor decomposition.
result Framework provides theoretical guarantees and outperforms state-of-the-art techniques.
The paper extends metrics and solitons on toric Fano manifolds with irregular Sasaki-Einstein metrics.
problem Extension of metrics and solitons on toric Fano manifolds with irregular Sasaki-Einstein metrics.
method Verification of the extension of momentum construction of Kaehler-Einstein metrics and Kaehler-Ricci solitons on the total space of positive rational powers of the canonical line bundle.
result The extended metric along the zero section has an expression that can be extended to the total space, and restricts to a transversely Kaehler-Einstein (Sasakian eta-Einstein) metric.
Paper tackles estimating initial conditions of spatio-temporal processes from sparse data.
problem Estimating initial conditions of spatio-temporal advection-diffusion processes from sparse data.
method Regularized convex optimization problem with Alternating Direction Method of Multipliers.
result Efficient solutions for non-uniform and shifted uniform sampling schemes.
Manifold learning offers nonlinear dimensionality reduction of high-dimensional datasets. In this paper, we bring geometry processing to bear on manifold learning by introducing a new approach based on metric connection for generating a quasi-isometric, low-dimensional mapping from a sparse and irregular sampling of an…
We study triangulations T defined on a closed disc X satisfying the following condition: In the interior of X, the valence of all vertices of T except one of them (the irregular vertex) is 6. By using a flat singular Riemannian metric adapted to T, we prove a uniqueness theorem when the valen…
The paper discusses new Lagrangian constructions and examples.
problem Exploring new Lagrangian constructions in complex projective spaces.
method Generalized Delaunay construction among minimal Lagrangians.
result Uncountably many new special Lagrangian cones found.
Paper connects Painlevé VI equation to irregular systems, solving monodromy data.
problem Solving monodromy data for irregular systems related to Painlevé VI.
method Expressed Frobenius integrability in terms of PVI, computed monodromy data for coalescing eigenvalues.
result Computed monodromy data for transcendentals holomorphic at critical points of PVI.
We describe the moduli spaces of meromorphic connections on trivial holomorphic vector bundles over the Riemann sphere with at most one (unramified) irregular singularity and arbitrary number of simple poles as Nakajima's quiver varieties. This result enables us to solve partially the additive irregular Deligne-Simpson…