Cut-DeepONet handles discontinuities and sharp transitions in neural operators.
problem Neural operators struggle with discontinuities and sharp transitions in PDEs.
method Two-stage training framework that explicitly models discontinuities via a lifting strategy and input-dependent discontinuity prediction.
result Cut-DeepONet outperforms state-of-the-art methods on benchmark PDEs with low-resolution datasets.
We develop a novel multi-fidelity framework that goes far beyond the classical AR(1) Co-kriging scheme of Kennedy and O'Hagan (2000). Our method can handle general discontinuous cross-correlations among systems with different levels of fidelity. A combination of multi-fidelity Gaussian Processes (AR(1) Co-kriging) and …
New method handles complex systems with discontinuous, heavy-tailed noise.
problem Handling discontinuous, heavy-tailed Lévy noise in stochastic systems.
method Developed nonlocal Kramers-Moyal formulas for SDEs with multiplicative Lévy noise.
result Validated framework for discovering interpretable SDE models from data.
Develops LF-PPL for non-differentiable models with automatic boundary checks.
problem Handling non-differentiable models in probabilistic programming.
method Introduces LF-PPL with automatic boundary checks and a formalism ensuring measure zero discontinuities.
result Demonstrates efficient inference for non-differentiable models using DHMC.
Proposes a new adaptive design strategy for discontinuous regression functions.
problem Designing input variables for discontinuous regression functions.
method Sequential adaptive design strategy using statistical properties.
result Effective design points selection for discontinuous regression functions.
Active learning improves GP regression on complex, high-dimensional data.
problem Improving Gaussian Process regression in high-dimensional spaces with discontinuous functions.
method Combines manifold learning with active learning to optimize data selection and reduce dimensionality.
result Superior performance over random learning in synthetic data experiments.
SMART combines decision trees and MARS for better regression modeling.
problem High variance in decision trees for continuous relationships, poor performance in MARS for discontinuities.
method SMART uses a decision tree to identify subsets with distinct continuous relationships, then applies MARS to fit these relationships independently.
result SMART improves regression performance over state-of-the-art methods in capturing discontinuities and continuous relationships.
This work uses diffusion models for accurate signal recovery from semi-parametric models.
problem Recovering signals from semi-parametric single index models with discontinuous link functions.
method Proposes an efficient reconstruction method using diffusion models that requires one round of sampling and inversion.
result Demonstrates more accurate reconstructions with fewer evaluations compared to competing methods.
New method for causal inference in survival outcomes using RDD.
problem Censoring in time-to-event analyses.
method Nonparametric approach with doubly robust censoring corrections.
result Higher efficiency and robustness to misspecification.
Proves nonemptyness of domains for specific group actions.
problem Nonemptyness of domains of proper discontinuity for Anosov groups of affine Lorentzian transformations.
method Proof of nonemptyness of domains of proper discontinuity.
result Proves nonemptyness of domains for Anosov groups of affine Lorentzian transformations.
The square root of Fredholm determinants causes numerical instabilities in option pricing models.
problem Numerical instabilities in Fourier-based option pricing for the Volterra Stein-Stein model.
method Characterization of determinant crossing behavior, derivation of transform to handle crossings, efficient algorithms.
result Significant improvement in accuracy and reduction in computational cost for Fourier-based pricing.
Deep learning speeds up material property quantification using stress waves.
problem Quantifying material properties from stress waves in complex media.
method Surrogate deep learning FWI scheme trained on random sampled properties and local minima.
result Demonstrates feasibility of deep learning for high-accuracy material property estimation.
We consider the deformation of a discontinuous group acting on the Euclidean space by affine transformations. A distinguished feature here is that even a `small' deformation of a discrete subgroup may destroy proper discontinuity of its action. In order to understand the local structure of the deformation space of disc…
Study proves existence of equilibrium in incomplete economies with discontinuous volatility.
problem Existence of incomplete Radner equilibrium with nondegenerate endogenous volatility.
method Established existence of solution for Markovian quadratic BSDEs with discontinuous generators using unique continuation and backward uniqueness.
result Existence of incomplete Radner equilibrium with nondegenerate endogenous volatility.
New domains of discontinuity found for Anosov representations.
problem Understanding Anosov representations acting on homogeneous spaces.
method Constructing open domains of discontinuity for Anosov representations acting on specific homogeneous spaces.
result Describes the largest possible open domains of discontinuity for Zariski dense Anosov representations.
As early as 1972, Penrose - in a purely formal way - introduced a "discontinuous coordinate transformation", which relates a continuous representation of the metric of impulsive pp-waves to a discontinuous one. On the basis of the invertibility concept for generalized functions developed recently by the first author, w…
A common analytical problem in neuroscience is the interpretation of neural activity with respect to sensory input or behavioral output. This is typically achieved by regressing measured neural activity against known stimuli or behavioral variables to produce a "tuning function" for each neuron. Unfortunately, because …
Study the discontinuity of functions not embeddable in Euclidean space.
problem Understanding discontinuity of non-embeddable functions.
method Define a modulus of discontinuity and establish lower bounds.
result Quantified nonembeddability results and topological Tverberg theorem.
Bayesian nonparametric discontinuity design improves causal inference without randomization.
problem Causal inference in non-randomized settings with additional assumptions.
method Bayesian model comparison and Gaussian process regression.
result BNDD can detect discontinuities of any order and spectral features.
Study new symmetries in non-symmetric spaces and discontinuous groups.
problem Analyze symmetries in non-symmetric homogeneous spaces and discontinuous groups.
method Investigate discrete series, discontinuous groups, and analysis on pseudo-Riemannian spaces.
result New insights into symmetries of non-symmetric homogeneous spaces and discontinuous groups.
Paper finds surface groups can deform in reductive symmetric spaces.
problem Finding deformations of discontinuous groups in reductive symmetric spaces.
method Analyzing Zariski dense surface subgroups and their deformations.
result Surface groups of high genus can deform in reductive symmetric spaces.
A new method for unsupervised disentanglement using axis-aligned cliffs.
problem Unsupervised disentanglement of latent factors under nonlinear maps.
method Encouraging axis-aligned discontinuities (cliffs) in the estimated density of factors.
result Cliff method outperforms baselines on disentanglement benchmarks.
Donors who defer their donations volunteer less in the future.
problem Volunteer labor can be less beneficial to charities than its costs.
method Regression discontinuity design with a procedure to handle manipulation.
result Donor manipulation invalidates standard regression discontinuity design, but a new method provides partial identification bounds.
New method estimates active subspaces for jump-discontinuous functions.
problem Estimating active subspaces for discontinuous functions like ABMs.
method Extending active subspaces to discontinuous functions, using Gaussian process.
result Identifies important parameters in ABM simulations of refugee movement.
This article gives an up-to-date account of the theory of discrete group actions on non-Riemannian homogeneous spaces. As an introduction of the motifs of this article, we begin by reviewing the current knowledge of possible global forms of pseudo-Riemannian manifolds with constant curvatures, and discuss what kind of …
We propose an approach to address two issues that commonly occur during training of unsupervised GANs. First, since GANs use only a continuous latent distribution to embed multiple classes or clusters of data, they often do not correctly handle the structural discontinuity between disparate classes in a latent space. S…
The first known example of a complete Riemannian manifold whose isoperimetric profile is discontinuous is given.
Paper analyzes error in stochastic approximation for discontinuous functions.
problem Estimating expected error in discontinuous stochastic approximation.
method Uses finite differences and O(n−1/5) error estimate for discontinuous functions. result Achieves error estimate of O(n−1/5) for discontinuous stochastic representation. Bayesian emulator tackles models with discontinuities efficiently.
problem Uncertainty quantification of models with multiple discontinuities.
method TENSE framework, designed correlation structures, single emulator object.
result Efficient emulation of complex models with multiple discontinuities.
We characterise completely when limit sets, as parametrised by Cannon-Thurston maps, move discontinuously for a sequence of algebraically convergent quasi-Fuchsian groups.
We show that there is a complete connected 2-dimensional Riemannian manifold with discontinuous isoperimetric profile, answering a question of Nardulli and Pansu.
We develop a general term structure framework taking stochastic discontinuities explicitly into account. Stochastic discontinuities are a key feature in interest rate markets, as for example the jumps of the term structures in correspondence to monetary policy meetings of the ECB show. We provide a general analysis of …
Study proves rigid spectral properties of planets with metric discontinuities.
problem Establishing spectral rigidity for spherically symmetric planets with discontinuities.
method Novel trace formula applied to two wave types in spherically symmetric manifolds with boundary and interior interfaces.
result Spectral rigidity of spherically symmetric planets with discontinuities is proven.
In this paper, we present a method for the accurate estimation of the derivative (aka.~sensitivity) of expectations of functions involving an indicator function by combining a stochastic algorithmic differentiation and a regression. The method is an improvement of the approach presented in [Risk Magazine April 2018]. T…
We study the properly discontinuous and isometric actions on the unit sphere of infinite dimensional Hilbert spaces and we get some new examples of Hilbert manifold with costant positive sectional curvature. We prove some necessary conditions for a group to act isometrically and properly discontinuously and in the case…
This work models overnight rates with jumps and discontinuities, extending classical short-rate models.
problem Capturing the jump behavior and discontinuities in overnight rates for accurate modeling.
method Developed a term structure modeling framework based on overnight rates, accommodating stochastic discontinuities.
result Simple specifications can capture the jump behavior of overnight rates, and explicit valuation formulas are provided.
The study explores deformations of discrete subgroups in non-compact homogeneous spaces.
problem Addressing the proper discontinuity of discrete subgroups in non-compact homogeneous spaces.
method Classification results for deformations of standard discontinuous groups in pseudo-Riemannian homogeneous spaces.
result Conditions for local rigidity and Zariski-dense deformations in standard quotients.
Paper analyzes SGHMC for non-convex optimization with discontinuous gradients.
problem Training neural networks with ReLU activation.
method Non-asymptotic convergence analysis of SGHMC with discontinuous gradients.
result Explicit upper bounds for expected excess risk in non-convex optimization.
This paper tackles discontinuous neural networks for better approximation of piecewise continuous functions.
problem Limitation of neural networks in approximating piecewise continuous functions due to discontinuities.
method Proposes a decoupled two-step procedure to train a discontinuous deep neural network model.
result Provides approximation guarantees for the proposed model in piecewise continuous function spaces.
In the present paper, we prove that no infinite group acts isometrically, effectively, and properly discontinuously on a certain class of Lorentzian manifolds that are not necessarily homogeneous.
Framework uses deep learning and statistical models to solve PDEs with discontinuous coefficients.
problem Solving PDEs with discontinuous coefficients.
method Two-stage physics-informed deep learning and statistical mixture models.
result Framework achieves adaptability and accurate parameter identification.
In this article we study properly discontinuous actions on Hilbert manifolds giving new examples of complete Hilbert manifolds with nonnegative, respectively nonpositive, sectional curvature with infinite fundamental group. We also get examples of complete infinite dimensional Kähler manifolds with positive holomorphic…
Estimates discontinuous optimal transport maps between a discrete and continuous distribution.
problem Estimating discontinuous optimal transport maps between a discrete and continuous distribution.
method Entropic optimal transport estimator, computationally efficient.
result The estimator converges at the minimax-optimal rate n−1/2 in the semi-discrete setting. Let X be a CAT(0) space, and G a discrete cyclic group of isometries of X. We investigate the domain of discontinuity for the action of G on the boundary ∂X.
We study the action of the group of polynomial automorphisms of C^n (n>2) which preserve the Markoff-Hurwitz polynomial H(x):= x_1^2 + x_2^2 + ... + x_n^2 - x_1 x_2 ... x_n. Our main results include the determination of the group, the description of a non-empty open subset of C^n on which the group acts properly discon…
RLGP model improves robustness and accuracy for discontinuous response surfaces.
problem Challenges in modeling abrupt jumps and discontinuities in response surfaces.
method Integrates adaptive nearest-neighbor selection with robustification mechanism.
result Consistently delivers high predictive accuracy and robustness in higher dimensions.
Motivated by the work of McCarthy and Papadopoulos for subgroups of mapping class groups, we construct domains of proper discontinuity in the compactified Outer space and in the projectivized space of geodesic currents for any "sufficiently large" subgroup of Out(FN) (that is, a subgroup containing a hyperbolic iwip…
The paper compares inserting and stretching points for grid refinement near critical points.
problem Decreased accuracy of finite difference methods near discontinuities.
method Comparison of inserting and stretching points for grid refinement near critical points.
result Proposes a new fast and simple stretching function.