Discrete-AIR model identifies objects in images with interpretable latent codes.
problem Identifying objects in images without labeled data.
method Recurrent Auto-Encoder with structured latent distributions for discrete, continuous, and spatial attention.
result Discrete-AIR model uses minimal latent variables for efficient inference.
New method for estimating spatial associations with discrete data, even under model misspecification.
problem Estimating associations between covariates and discrete responses with spatial variability and nonrandom sampling.
method Proposes a novel approach to handle spatially varying noise, provides a proof of consistency, and uses a delta method argument.
result Empirically shows reliable confidence intervals compared to standard methods, even with model misspecification.
Graph neural networks improve residential location choice predictions.
problem Capturing spatial dependence in discrete choice models.
method Graph Neural Networks (GNN) for analyzing spatial alternatives.
result GNN-DCMs outperform classical models in residential location choice predictions.
EFDM models spatial point processes with variable cardinality using existence variables.
problem Challenges in extending diffusion models to variable-cardinality spatial point processes.
method Existence-field diffusion model (EFDM) that jointly models spatial locations and cardinality without discrete transitions.
result EFDM achieves improved modeling capability on datasets with varying cardinality.
We present a simple one-parameter model for spatially localised evolving agents competing for spatially localised resources. The model considers selling agents able to evolve their pricing strategy in competition for a fixed market. Despite its simplicity, the model displays extraordinarily rich behavior. In addition t…
A new neural approach for generating origin-destination matrices in ABMs.
problem Challenges in generating origin-destination matrices for ABMs, including discretisation errors and inability to explore multimodal distributions.
method A computationally efficient framework that learns trip intensity through a neural differential equation, operating directly on the discrete combinatorial space.
result Outperforms prior art in terms of reconstruction error and ground truth matrix coverage, at a fraction of the computational cost.
We discretize a cost functional for image registration problems by deriving Taylor expansions for the matching term. Minima of the discretized cost functionals can be computed with no spatial discretization error, and the optimal solutions are equivalent to minimal energy curves in the space of k k k -jets. We show that t…
Paper variates Navier-Stokes-Fourier system for thermodynamic consistency.
problem Modeling compressible fluid dynamics with thermodynamic constraints.
method Variational discretization with discrete exterior calculus.
result Derives a nonholonomic variational integrator for NSF system.
The convolution method for the numerical solution of forward-backward stochastic differential equations (FBSDEs), introduced in [21], uses a uniform space grid. In this paper we utilize a tree-like spatial discretization that approximates the BSDE on the tree, so that no spatial interpolation procedure is necessary. In…
Bayesian method improves segmentation accuracy with noisy labels.
problem Annotation errors in semantic segmentation due to mislabeling and spatial correlations.
method Approximate Bayesian estimation with spatially correlated discrete distributions and variational inference.
result The method achieves performance comparable to clean labels under moderate noise levels.
DINo forecasts PDEs with flexible extrapolation and adaptability.
problem Fixed discretizations limit real-world PDE forecasting.
method DINo uses implicit neural representations for continuous-time dynamics.
result DINo outperforms other neural PDE forecasters.
We consider the problem of estimating the topology of spatial interactions in a discrete state, discrete time spatio-temporal graphical model where the interactions affect the temporal evolution of each agent in a network. Among other models, the susceptible, infected, recovered ( S I R SIR S I R ) model for interaction events fal…
The paper studies singularities in discrete indefinite affine minimal surfaces.
problem Characterizing singularities in discrete indefinite affine minimal surfaces.
method Discretizing smooth curves and applying discrete Lelieuvre's formulas to study the resulting surfaces.
result The definition of singular edges and vertices in discrete asymptotic nets mirrors properties of smooth surfaces.
Survey on matrix hydrodynamics, a 2D fluid model.
problem Modeling 2D incompressible fluids.
method Spatial discretization via quantization theory.
result Basic demonstration of matrix hydrodynamics.
New methods solve complex financial equations.
problem Solving backward stochastic differential equations driven by continuous-time Markov chains.
method Multi-stage Euler-Maruyama methods and multilevel spatial discretization.
result Efficiently solved stiff Markov BSDEs.
New framework for 3D spatial topology enumeration and identification.
problem Efficient navigation through complex engineering system topologies.
method Mathematical spatial graph theory to represent, enumerate, and identify unique topological classes.
result Identification of distinctive 3D topological classes for engineering systems.
Earth observation embeddings can convert discrete biome maps into continuous representations that better capture ecological variation.
problem Biome maps impose categorical boundaries that compress continuous variation in biotic communities.
method Fit a linear classifier on Earth observation embeddings to predict biome labels.
result Continuous biome representation outperforms discrete biome labels for predicting species occurrence.
A new method for solving time-dependent PDEs using Gaussian processes.
problem Solving time-dependent and non-linear PDEs with noisy data and uncertainty quantification.
method Numerical Gaussian processes with covariance functions from time-dependent PDEs, using Gaussian process priors for temporal discretization.
result Accurate approximations of latent solutions with uncertainty propagation, even for long time integration.
We propose an efficient method for estimating covariate effects in doubly-stochastic spatial models.
problem Computational demands and restrictive assumptions in existing doubly-stochastic spatial models.
method Penalized regression method for estimating covariate effects in doubly-stochastic point processes.
result Consistency and asymptotic normality of the covariate effect estimates achieved despite model misspecification.
Sparse-mode DMD disambiguates local and global modes in spatiotemporal data.
problem Disambiguating local and global modes in spatiotemporal data.
method Sparse-mode DMD with sparsity-promoting regularization.
result Explicitly constructs discrete and continuous spectra.
Lin-DBSCAN is a fast density-based clustering algorithm for spatial data.
problem Efficient clustering of large datasets without prior knowledge of cluster number and shape.
method Grid-based scan and merge approach to a discrete density model of DBSCAN.
result Lin-DBSCAN outperforms DBSCAN in efficiency and validity for spatial data clustering.
Enhanced visibility forecasts using CAMS data improve accuracy.
problem Improving the accuracy of visibility predictions in weather forecasts.
method Statistical post-processing with historical observations and CAMS forecasts.
result Post-processed forecasts with CAMS data are substantially superior to raw and climatological predictions.
Paper presents voxel graph operators for vector data models.
problem Efficient conversion and analysis of geometric models.
method Topological voxelization, graph construction, differential operator derivation.
result Discrete differential and integral operators from voxel complexes.
Extends Zeitlin's model to 3-D axisymmetric Euler equations.
problem Preserving geometric structure in 3-D Euler equations.
method Axisymmetric discretization of 3-D Euler equations on the 3-sphere.
result First discretization of 3-D Euler equations preserving geometric structure.
The stability and robustness of compact schemes for parabolic PDEs are analyzed.
problem Stability and robustness of compact schemes for solving parabolic PDEs.
method Compact spatial discretization, Crank-Nicolson temporal discretization, eigenvalue analysis of amplification matrix.
result An upper bound on the condition number of the amplification matrix is derived, showing stability.
Turnpike results for risk tolerance in incomplete markets under time-monotone criteria.
problem Turnpike results for risk tolerance in incomplete markets under time-monotone criteria.
method Time-monotone forward performance criteria, analysis of limits, dependence on measure support.
result Temporal and spatial limits do not coincide and depend on measure support.
In this article we propose a novel approach to reduce the computational complexity of various approximation methods for pricing discrete time American options. Given a sequence of continuation values estimates corresponding to different levels of spatial approximation and time discretization, we propose a multi-level l…
Develops a new Bayesian inference method for discrete data.
problem Computational challenges in discrete state spaces, especially intractable likelihoods.
method Uses a discrete Fisher divergence to update beliefs about model parameters, circumventing the intractable normalising constant.
result Establishes statistical properties of the generalised posterior and proposes a calibration approach.
Novel hybrid model combines image feature discovery and topic modeling for marine robot mission data.
problem Insufficient analysis of robot mission data due to data complexity and lack of suitable models.
method Convolutional autoencoders for feature discovery in images and Bayesian nonparametric topic models for thematic structure.
result Hybrid model outperforms state-of-the-art approaches in unsupervised seafloor terrain characterization.
Deep learning models simulate complex karst network patterns.
problem Complex karst network patterns due to hydrogeological conditions.
method Graph generative models (GraphRNN and G-DDPM) to capture topological and spatial properties.
result Stochastic simulation of karst networks across various formations.
Develops a new model for spatio-temporal data using imitation learning.
problem Capturing complex spatio-temporal dependence in discrete event data.
method NEST point process model with imitation learning for efficient model fitting.
result The imitation learning approach leads to more robust and interpretable results.
A natural approach to analyze interaction data of form "what-connects-to-what-when" is to create a time-series (or rather a sequence) of graphs through temporal discretization (bandwidth selection) and spatial discretization (vertex contraction). Such discretization together with non-negative factorization techniques c…
New method preserves MHD equations on sphere without costly matrix exponentials.
problem Discretizing MHD equations on sphere for numerical simulations.
method Lie-Poisson discretization, geometric quantization, semi-direct product Lie algebras.
result Preserves Lie-Poisson structure and Casimir functions.
New method infers diffusion equations from sparse data.
problem Statistical inference of diffusion equations from limited data.
method Neural network-based estimators for drift and diffusion tensor.
result Statistical convergence guarantees for Hölder continuous processes.
Sharp Lipschitz bounds for flow-matching and diffusion models with optimal sampling rates.
problem Establishing optimal Lipschitz regularity for flow-matching and diffusion models.
method Sharp Lipschitz regularity theory for flow-matching vector fields and diffusion-model scores.
result Achieves optimal sampling rate of d / N \sqrt{d}/N d / N for Euler-type samplers in dimension d d d . Latent Dirichlet Allocation models discrete data as a mixture of discrete distributions, using Dirichlet beliefs over the mixture weights. We study a variation of this concept, in which the documents' mixture weight beliefs are replaced with squashed Gaussian distributions. This allows documents to be associated with e…
DMSTF models spatio-temporal data with deep Markov priors.
problem Analyzing nonlinear multimodal spatio-temporal dynamics.
method Deep Markov spatio-temporal factorization with stochastic variational inference.
result DMSTF outperforms other methods in predictive performance and clustering.
New analysis improves convergence guarantees for diffusion-based samplers in Wasserstein distance.
problem Improving convergence guarantees for diffusion-based generative models.
method Simple framework to analyze discretization, initialization, and score estimation errors.
result First Wasserstein convergence bound for the Heun sampler and improved results for Euler sampler.
Researchers prove inequalities for reaction-diffusion systems using a new curvature-dimension condition.
problem Proving Li-Yau and Harnack inequalities for systems of linear reaction-diffusion equations.
method Introducing a hybrid curvature-dimension condition and proving a differential Harnack estimate.
result A Harnack inequality holds under the hybrid curvature-dimension condition C D h y b ( 0 , d ) CD_{hyb} (0,d) C D h y b ( 0 , d ) with d < ∞ d<\infty d < ∞ . Space2Vec learns multi-scale spatial representations from grid cell insights.
problem Encoding spatial features with varying scales from GIS data.
method Proposes Space2Vec, a multi-scale representation learning model using grid cell insights.
result Space2Vec outperforms baselines in predicting POI types and image classification with geo-locations.
Paper analyzes tech adoption in financial networks, finding key leadership and diffusion dynamics.
problem Understanding technology adoption and network effects in financial systems.
method Developed a spatial-network framework with a master equation and Feynman-Kac representation.
result Found strong support for two-regime adoption dynamics and significant leadership in network central banks.
A new method uses coherent structure coloring to estimate model parameters more accurately than traditional methods.
problem Challenges in estimating model parameters from Lagrangian data in turbulent flows.
method Use coherent structure coloring (CSC) field to assess model skill and estimate model parameters.
result Error in the CSC field can accurately determine model parameters, while conventional methods fail.
Efficiently reconstructs spatio-temporal Gaussian processes using Kalman filtering.
problem Non-parametric reconstruction of spatio-temporal Gaussian processes from sparse and noisy data.
method Coupling GP regression and Kalman filtering for a finite-dimensional state-space representation.
result Kalman filter state at instant t k t_k t k represents a sufficient statistic for estimating the process at any t ≥ t k t \geq t_k t ≥ t k . flexBART improves BART for categorical predictors by creating flexible tree partitions.
problem Limitation of BART in handling categorical predictors with one-hot encoding.
method flexBART re-implements BART with regression trees that can assign multiple levels to both branches of a decision tree node, and proposes a new decision rule prior for spatial data.
result flexBART often yields improved predictive performance and scales better to larger datasets than existing BART implementations.
Automated method bounds causal effects in discrete data.
problem Partial identification of causal effects in discrete settings.
method Polynomial programming and dual relaxation for automated bounds.
result Algorithm provides guaranteed non-sharp and ε ε ε -sharp bounds. DICE learns population dynamics from discrete samples.
problem Learning smooth population dynamics from discrete data.
method Discrete Inverse Continuity Equation (DICE) method.
result DICE models are stable and generate representative samples.
Proposes continuous convolution layers for flexible feature map resizing.
problem Fixed stride limitations in discrete convolution layers.
method Introduces Continuous Convolution (CC) layers that use learned continuous functions.
result Dynamic and consistent resizing of feature maps at any scale, non-integer and axis-dependent.
EDGI improves sample efficiency and generalization in tasks with spatial and temporal symmetries.
problem Sample inefficiency and poor generalization in tasks with geometric symmetries.
method Equivariant Diffuser framework, SE(3)xZxSn-equivariant diffusion model.
result EDGI is more sample efficient and generalizes better than non-equivariant models.