Extracts coarse-grained PDEs from microscopic simulations.
problem Discovering effective PDEs for macro-scale processes from microscopic data.
method Combining neural networks with equation-free numerics and data-driven approaches.
result Efficiently discovers macro-scale PDEs from microscopic simulations.
Local Neural Operators enable efficient system-level analysis of complex PDEs.
problem System-level analysis of large-scale dynamical systems using neural operators.
method Integrating local Neural Operators with Krylov subspace iterative methods for stability and bifurcation analysis.
result Demonstrated effectiveness of local Neural Operators in fixed-point, stability, and bifurcation analysis of nonlinear PDEs.
TURB-Rot provides a large database of turbulent rotating flow snapshots for research.
problem Lack of large-scale, high-resolution datasets for turbulent rotating flows.
method Direct Numerical Simulations of Navier-Stokes equations with rotation.
result Provides a diverse set of 300K complex images and fields for testing.
Derives PDEs from data using manifold learning and neural networks.
problem Identifying PDEs from unknown variables and dynamics.
method Combines manifold learning (Diffusion Maps) and neural networks.
result Emergent space identification connects with multiscale computation.
Study proves all free boundary CMC annuli are of finite type.
problem Free boundary constant mean curvature annuli in the unit ball.
method Adapted Sklyanin's K-matrix formalism to sinh-Gordon equation.
result All free boundary CMC annuli are of finite type.
The inference of correlated signal fields with unknown correlation structures is of high scientific and technological relevance, but poses significant conceptual and numerical challenges. To address these, we develop the correlated signal inference (CSI) algorithm within information field theory (IFT) and discuss its n…
Smooth solutions up to evolving free boundaries for degenerate equations.
problem Degenerate parabolic equations with evolving free boundaries.
method Smooth short-time existence using linear degenerate equations on a fixed domain.
result Smoothness up to the free boundary for the p-Laplacian evolution equation and α-Gauss curvature flow. This paper analyzes optimal consumption strategies for loss-averse investors with multiplicative habit formation.
problem Optimal consumption strategies for loss-averse investors with multiplicative habit formation.
method The study uses a concave envelope of the S-shaped utility function and a nonlinear free boundary problem to analyze the HJB equation.
result The paper provides optimal consumption and investment policies in feedback form.
The wave equation (free boson) problem is studied from the viewpoint of the relations on the symplectic manifolds associated to the boundary induced by solutions. Unexpectedly there is still something to say on this simple, well-studied problem. In particular, boundaries which do not allow for a meaningful Hamiltonian …
Solves a general class of free boundary Monge-Ampère equations.
problem Optimal transport with degenerate densities and geometric problems.
method Analyzes a specific class of Monge-Ampère equations and their applications.
result Solves the equations for a general class, including applications to optimal transport and geometric problems.
Framework detects tipping points in complex systems using ML.
problem Detecting tipping points in complex, emergent systems.
method Combining manifold learning, neural networks, and Gaussian processes.
result Reduced-order models for mesoscopic and mean-field dynamics.
We demonstrate the application of an algorithmic trading strategy based upon the recently developed dynamic mode decomposition (DMD) on portfolios of financial data. The method is capable of characterizing complex dynamical systems, in this case financial market dynamics, in an equation-free manner by decomposing the s…
LSS learns molecular trajectories from MD data.
problem Limited integration time steps in MD simulations.
method Three deep learning networks for slow collective variables, dynamics, and configuration reconstruction.
result Generates ultra-long synthetic folding trajectories.
Probabilistic numerics expands numerical tasks with black box methods.
problem Difficult conditioning of random variables in numerical tasks.
method Construct probabilistic numerical methods based on final outputs, extrapolating limiting quantities.
result Higher orders of convergence achieved in various numerical tasks.
Study disproves a generalized numerical criterion for certain pairs.
problem Generalized numerical criterion for pairs
method Provided counterexamples
result Negative answer to the generalized numerical criterion problem
New method combines ODE filters and numerical quadrature to propagate model uncertainty.
problem Propagation of model uncertainty in ODE solutions with uncertain parameters.
method Combining ODE filters with numerical quadrature.
result Effective propagation of both numerical and parametric uncertainty.
Efficient numerical method for time-fractional Black-Scholes model.
problem Solving time-fractional Black-Scholes equations for European options.
method Crank-Nicolson discretization for time, exponential B-spline for space.
result The proposed method is unconditionally stable and superior to existing approaches.
We deliver a call to arms for probabilistic numerical methods: algorithms for numerical tasks, including linear algebra, integration, optimization and solving differential equations, that return uncertainties in their calculations. Such uncertainties, arising from the loss of precision induced by numerical calculation …
The paper solves complex swing option pricing equations with numerical methods.
problem Valuation of swing options with jumps under a mean-reverting model.
method Proposes second-order numerical methods to solve PIDEs convection-dominated and with nonlocal integral terms.
result Numerical methods confirm second-order convergence behavior.
Study identifies numerical signs of blow-up in hydrodynamic equations.
problem Determining if numerical results of blow-up are genuine or artifacts.
method Geometrically consistent spatiotemporal discretization of complexified Euler equations.
result Identification of a signature based on supremum norm growth rates of vorticity.
We develop the theory of smooth principal bundles for a smooth group G, using the framework of diffeological spaces. After giving new examples showing why arbitrary principal bundles cannot be classified, we define D-numerable bundles, the smooth analogs of numerable bundles from topology, and prove that pulling ba…
FiNCAT tool automatically identifies financial numerals in documents.
problem Differentiating between in-claim and out-of-claim numerals in financial documents.
method Extracts context embeddings of numerals using BERT, then uses Logistic Regression to classify.
result Achieved a Macro F1 score of 0.8223 on validation set.
Proves representability of complex semigroup systems.
problem Representability of systems of proportionally modular numerical semigroups.
method Canonical equivariant resolution of weighted homogeneous surface singularities.
result Every system of proportionally modular numerical semigroups is representable.
In this manuscript we introduce numerical Gaussian process Kalman filtering (GPKF). Numerical Gaussian processes have recently been developed to simulate spatiotemporal models. The contribution of this paper is to embed numerical Gaussian processes into the recursive Kalman filter equations. This embedding enables us t…
Language models can predict numeric values as strings.
problem Regression tasks with numeric predictions.
method Causal sequence decoding models trained for next-token prediction.
result Decoder-based heads perform as well as standard heads in numeric regression tasks.
The paper analyzes numerical instability in variational flows and proposes a diagnostic method.
problem Numerical instability in variational flows affects sampling, density evaluation, and ELBO estimation.
method Treated variational flows as dynamical systems, used shadowing theory for theoretical guarantees, and developed a diagnostic procedure.
result Despite numerical instability, results from variational flows can be accurate enough for practical applications.
Study shows how numerical discretization affects reconstructions and parameter distributions in nano metrology.
problem Impact of numerical discretization on parameter reconstructions and model parameter distributions.
method Bayesian target vector optimization, finite element model, Gaussian process, stochastic machine learning surrogate models, Markov chain Monte Carlo sampler.
result Numerical discretization parameters impact the accuracy and distribution of reconstructed model parameters.
Paper introduces NumLLM for better financial text understanding with numeric variables.
problem Poor performance of existing financial large language models in numeric financial text.
method Constructed financial corpus, fine-tuned with LoRA modules, merged into foundation model.
result NumLLM achieves best performance on financial question-answering benchmark, especially with numeric questions.
We give (1) an upper bound on the denominators of numerical boundary slopes and (2) an upper bound on the differences between two numerical boundary slopes, for Montesinos knot exteriors.
Parallel-in-time solver reduces ODE simulation time from linear to logarithmic.
problem Efficiently solving ordinary differential equations (ODEs) with reduced computational cost.
method Formulated a parallel-in-time probabilistic numerical ODE solver using time-parallel formulation of iterated extended Kalman smoothers.
result Reduces span cost from linear to logarithmic in the number of time steps.
We provide notions of numerical effectiveness and numerical flatness for Higgs vector bundles on compact Kähler manifolds in terms of fibre metrics. We prove several properties of bundles satisfying such conditions and in particular we show that numerically flat Higgs bundles have vanishing Chern classes, and that they…
A new framework improves tensor completion accuracy by considering numerical priors.
problem Tensor completion accuracy loss due to ignoring numerical priors.
method Generalized CP Decomposition Tensor Completion (GCDTC) framework incorporating numerical priors.
result GCDTC framework outperforms state-of-the-arts in non-negative tensor completion.
Paper approximates fractional harmonic maps with numerical methods.
problem Approximating fractional harmonic maps with constraints and nonlocality.
method Weak compactness results and numerical methods for various PDEs.
result Convergence of numerical approximations for fractional harmonic maps.
End-to-end solution for recognizing handwritten numerals, avoiding traditional preprocessing steps.
problem Handwritten numeral string recognition with traditional preprocessing steps.
method YoLo-based model for automatic detection and recognition, avoiding heuristic-based preprocessing and segmentation.
result Proposed method reduces complexity and is a feasible end-to-end solution for numeral string recognition.
LLMs struggle with arithmetic tasks unless they use high numerical precision.
problem Improving arithmetical reasoning capabilities of LLMs.
method Theoretical analysis and empirical experiments on numerical precision.
result LLMs require high numerical precision to efficiently handle arithmetic tasks.
This paper tackles Bayesian system identification with probabilistic numerical methods.
problem Accurately modeling nonlinear dynamic systems from noisy data.
method Probabilistic Sequential Monte Carlo (SMC) combined with probabilistic numerical integration.
result Efficient identification of latent states and system parameters from noisy measurements.
Develops a numerical method for LRM strategies in BNS models with infinite active jumps.
problem Calculating locally risk-minimizing strategies for non-martingale BNS models with infinite active jumps.
method Modified Malliavin calculus expression and Monte Carlo method for non-martingale BNS models.
result Proposes a numerical method for LRM strategies in non-martingale BNS models with infinite active jumps.
Deep learning solves high-dimensional PDEs efficiently.
problem Solving high-dimensional Kolmogorov PDEs numerically.
method Reformulating as a statistical learning problem using Feynman-Kac formula.
result Single neural network learns entire family of PDEs.
In this Article, a fast numerical numerical algorithm for pricing discrete double barrier option is presented. According to Black-Scholes model, the price of option in each monitoring date can be evaluated by a recursive formula upon the heat equation solution. These recursive solutions are approximated by using Legend…
Study numerically flat foliations on Kähler manifolds, proving new splitting theorems.
problem Understanding foliations with numerically flat tangent bundles on Kähler manifolds.
method Analyzing the structure of foliations on compact Kähler manifolds, extending earlier results.
result Smooth foliations with numerically flat tangent bundles induce a decomposition of the ambient manifold's tangent bundle.
The paper defines and proves conditions for numerical semistability of smooth toric varieties.
problem Understanding the numerical semistability of smooth toric varieties.
method Analyzing the Chow/Hurwitz forms and applying toric degenerations.
result A necessary and sufficient condition for a smooth toric variety to be numerically semistable.
In this paper we present qualitative and quantitative comparison of various analytical and numerical approximation methods for calculating a position of the early exercise boundary of the American put option paying zero dividends. First we analyze their asymptotic behavior close to expiration. In the second part of the…
Recognizing written domain numeric utterances (e.g. I need $1.25.) can be challenging for ASR systems, particularly when numeric sequences are not seen during training. This out-of-vocabulary (OOV) issue is addressed in conventional ASR systems by training part of the model on spoken domain utterances (e.g. I need one …
The paper addresses numerical integration issues in SV models, proposing a fast regime switching algorithm.
problem Numerical integration challenges in SV models, especially with high precision and low computational time.
method Proposes a fast regime switching algorithm to determine when higher precision arithmetic is needed.
result Shows that numerical quadratures need to be carefully chosen based on model parameters and parameter values.
In this paper, we propose a verified numerical method for obtaining a sharp inclusion of the best constant for the embedding H01(Ω)↪Lp(Ω) on bounded convex domain in R2. We estimate the best constant by computing the corresponding extremal function using a verified numerical com…
Improved MLMC method for robust and efficient probability and density estimation.
problem Stability and poor complexity of MLMC for low-regularity functionals.
method Numerical smoothing combined with MLMC for deterministic quadrature methods.
result Significant improvement in strong convergence and robustness of MLMC method.
New method models dewetting of anisotropic particles using numerical techniques.
problem Modeling dewetting dynamics of particles with varying surface energies.
method Level set numerical approach with convolution kernels to handle anisotropic interfacial energies.
result Validated numerical scheme supports merging and splitting of interfaces.
In this paper, we study numerically flat holomorphic vector bundles over a compact non-Kähler manifold (X,ω) with the Hermitian metric ω satisfying the Gauduchon and Astheno-Kähler conditions. We prove that numerically flatness is equivalent to numerically effectiveness with vanishing first Chern number, semistabl…