archive
Every paper Pith has read. Search by title, abstract, or pith.
1525 papers in math.NA · page 5
-
Crank-Nicolson FEM conserves energy exactly for KGZ equations
A novel energy-conservation Crank-Nicolson finite element method for generalized Klein-Gordon-Zakharov equations
-
Stability radii bound safe perturbations in Hamiltonian DAEs
Characterization of stability radii for robustly asymptotically stable dissipative Hamiltonian differential-algebraic systems
-
Splitting scheme converges for wave maps at low regularity
A splitting scheme for the wave maps equation at low regularity
-
IPRM removes Gibbs ringing from fractional Fourier series
Resolving the Gibbs Phenomenon in Fractional Fourier Series via Inverse Polynomial Reconstruction
-
Contraction map on Legendre-reduced system recovers nonlinear Schrödinger initial data
Inverse initial data for nonlinear Schr\"odinger equation via Carleman estimates and the contraction principle
-
Random spectra match Muon on GPT-2 training
Muon is Not That Special: Random or Inverted Spectra Work Just as Well
-
Algorithm guarantees energy decrease for ferronematic states
An energy-decreasing algorithm for the finite element approximation of ferronematic equilibrium states
-
MHD projection sliced to 1D Brent minimization
Efficient Admissible Set Projection in Optimization-based Invariant-Domain-Preserving Limiters for Ideal MHD
-
Separable estimators tighten relaxations beyond McCormick
Relaxation via Separable Estimators: Arithmetic and Implementation
-
Unitaria composes quantum block encodings like NumPy arrays
Unitaria: Quantum Linear Algebra via Block Encodings
-
Bayesian linear solvers are special cases of affine PIMs
Affine Tracing: A New Paradigm for Probabilistic Linear Solvers
-
Coupled CO2-temperature model predicts building dynamics from sparse data
Data-driven moving-window Bayesian inference for transient CO2-temperature network models of buildings
-
Three method classes for MD transport coefficients each carry error bounds
Mathematical analysis and numerical methods for the computation of transport coefficients in molecular dynamics
-
Learning adaptive bases from data lifts spectral PDE operators
Don't Fix the Basis -- Learn It: Spectral Representation with Adaptive Basis Learning for PDEs
-
Perturbation correction converts Stefan optimization to convex and lifts accuracy 2-6x
PCELM: Perturbation-Correction Extreme Learning Machine for the Stefan problem
-
hp-FEM discretizes elastoplasticity with mixed variational forms
hp-Finite Elements for Elastoplasticity
-
PowerStep matches Adam on Transformers with half the optimizer memory
PowerStep: Memory-Efficient Adaptive Optimization via $\ell_p$-Norm Steepest Descent
-
JAX tracing system unifies data and physics losses for neural operators
jNO: A JAX Library for Neural Operator and Foundation Model Training
-
Neural TGV² tomography cuts errors 33-44 percent on layered and faulted models
Total Generalized Variation regularization closes the gap between neural-eld and classical methods in seismic travel-time tomography
-
O(M) algorithm computes Helmholtz Fourier modes independently of k
Fast Evaluation of the Azimuthal Fourier Modes of the 3D Helmholtz Green's Function and Their Derivatives
-
MCMC reaches O(ε²) error for time-changed SDE parameters at O(ε^{-2} log²ε) cost
Parameter Estimation for Partially Observed Time-Changed SDEs
-
Reduced elliptic interface error depends only on interface data accuracy
Interface Reduction for Elliptic Interface Problems with Conservative Flux Reconstruction
-
Fast sketching accelerates power method for low-rank approximations
Accelerating Power Method with Fast Sketching for Stronger Low-Rank Approximation
-
Neural networks enrich FEM to reduce degrees of freedom for oscillations
Neural enrichment finite element method: A hybrid framework for problems with strong oscillations or interface problems
-
Active Flux scheme reformulated for stronger dissipation
On Enhancing the Dissipative Behavior of Active Flux Advection Schemes
-
Kernel ridge regression learns PDE solution operators without paired data
Kernel Learning of PDE Solution Operators
-
Semi-implicit FEM keeps saturations between 0 and 1 for Richards equation
Discrete positivity and maximum principles for a finite element discretization of the Richards equation
-
History-aware operator halves rollout error for memory PDEs
HS-FNO: History-Space Fourier Neural Operator for Non-Markovian Partial Differential Equations
-
History-space neural operator halves rollout error for memory PDEs
HS-FNO: History-Space Fourier Neural Operator for Non-Markovian Partial Differential Equations
-
Boundary integrals model waves around moving obstacles in varying media
A boundary integral method for wave scattering in a heterogeneous medium with a moving obstacle
-
Boundary integral method models waves past moving objects in varied media
A boundary integral method for wave scattering in a heterogeneous medium with a moving obstacle
-
Patchwise Fourier extensions achieve linear cost on curved domains
A Patchwise Local Fourier Extension Method for Function Approximation on General Two-Dimensional Domains
-
Neural correction makes low-budget Monte Carlo PDE solves match 1000x compute
MC$^2$: Monte Carlo Correction for Fast Elliptic PDE Solving
-
Algebraic multiscale method converges independently of network geometry
Efficient Multiscale Methods for Highly Heterogeneous Spatial Network Models
-
Variational equation governs least-squares backward error
A Variational Equation and Lower Bound for the Linear Least-Squares Backward Error
-
Gauss-Seidel NPDo updates converge for principal joint diagonalization
An NPDo Approach for Principal Joint SVD-type Block Diagonalization
-
New Rao-Blackwellization cuts variance in MCMC light transport
Rao-Blackwellized Markov chain Monte Carlo Light Transport
-
Dense Lie algebra yields local universal contact integrators
Local Universal Splitting Integrators for Contact Hamiltonian Systems
-
Nonlinear jumps reduced to one scalar equation
A scalar interface reduction for nonlinear interface problems
-
Schwarz framework refines MPM locally with up to 9x speedup
An Overlapping Schwarz Space-Time Refinement Framework for Material Point Method
-
Local Legendre frames give stable approximation from equispaced data
Local Legendre Frame Approximation from Equispaced Data
-
Spectral scheme approximates fractional diffusion on anisotropic domains
A time dependent fractional order diffusion equation with constant diffusivity matrix
-
Learned chart boosts neural PDE accuracy by 27%
CATO: Charted Attention for Neural PDE Operators
-
Karhunen-Loève series uses covariance eigenfunctions for optimal random field series
A Primer on the Karhunen-Lo\`eve Expansion
-
Diffusion Restore makes MCMC light transport real-time
Diffusion Restore: Real-Time Markov Chain Monte Carlo Light Transport
-
Diffusion Restore achieves real-time MCMC light transport
Diffusion Restore: Real-Time Markov Chain Monte Carlo Light Transport
-
Diffusion dynamics make MCMC light transport run in real time
Diffusion Restore: Real-Time Markov Chain Monte Carlo Light Transport
-
Finite measurements cause non-unique minimizers in neural variational methods
Non-Uniqueness of Solutions in Neural Variational Methods
-
Finite measurements yield non-unique minimizers in neural variational methods
Non-Uniqueness of Solutions in Neural Variational Methods
-
Rough paths solve signature and Schwinger-Dyson kernel equations
Signature Kernel and Schwinger-Dyson Kernel Equations as Two-Parameter Rough Differential Equations