Study nonlinear heat equation gradient estimates and applications.
problem Gradient estimates for nonlinear heat equation.
method Elliptic gradient estimates for a nonlinear -heat equation.
result Obtain gradient estimates for positive solutions.
On-device research index
arXiv research
A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
169,341 papers · 148 categories
Trend · papers per month
48 results for “nonlinear estimators”
The paper provides estimates for positive solutions to a nonlinear equation under geometric flow.
problem Analyzing positive solutions to a nonlinear equation under geometric flow.
method Gradient estimates for positive solutions under geometric flow on manifolds.
result Gradient estimates for positive solutions to a nonlinear equation under geometric flow.
Proposes a new method for nonlinear Bayesian updates using ensemble kernel regression.
problem Nonlinear and non-Gaussian Bayesian updates for complex systems.
method Combines Kalman filtering for observed components and kernel density estimation for unobserved components, with subsampling and clustering.
result Reduces estimation errors in highly nonlinear scenarios compared to standard linear updates.
The paper develops adaptive deep learning methods for nonlinear time series models.
problem Estimating mean functions of non-stationary and nonlinear time series models.
method Develops non-penalized and sparse-penalized DNN estimators for general non-stationary time series, derives minimax lower bounds, and shows the sparse-penalized DNN estimator is adaptive and optimal.
result Sparse-penalized DNN estimator achieves minimax optimal rates for many nonlinear AR models.
Sharp Lipschitz bounds and gradient estimates for fully nonlinear parabolic equations.
problem Understanding moduli of continuity for fully nonlinear parabolic equations.
method Proving moduli of continuity of viscosity solutions are subsolutions of one-dimensional parabolic equations.
result Sharp Lipschitz bounds and gradient estimates for fully nonlinear parabolic equations with bounded initial data.
The paper extends Li-Yau-Hamilton estimates to evolving Kähler metrics and nonlinear heat equations.
problem Deriving estimates for nonlinear heat equations on evolving Kähler metrics.
method Generalized matrix Li-Yau-Hamilton estimates to Kähler manifolds with evolving metrics and nonlinear heat equations.
result Extended Li-Yau-Hamilton estimates to evolving Kähler metrics and nonlinear heat equations.
Gradient estimates for solutions to a specific nonlinear equation on Riemannian manifolds.
problem Estimating gradients of solutions to a nonlinear elliptic equation on Riemannian manifolds.
method Analyzing the equation Δu + cu^α = 0 to derive gradient estimates.
result Gradient estimates for positive solutions to the given equation on complete Riemannian manifolds.
Paper connects contrastive learning to MI maximization and establishes robust methods for nonlinear ICA and subspace estimation.
problem Understanding and improving unsupervised representation learning and density ratio estimation.
method The paper connects contrastive learning to MI maximization, establishes new recovery conditions for nonlinear ICA, and proposes a practical outlier-robust method for nonlinear subspace estimation.
result The proposed methods can be seen as maximizing MI, performing nonlinear ICA, or estimating nonlinear subspaces, and are robust to outliers.
Optimistic estimate predicts best fitting performance of nonlinear models.
problem Evaluating the potential of nonlinear models in fitting.
method Proposes an optimistic estimate to quantify the smallest sample size for fitting nonlinear models.
result Predicts specific subsets of targets that can be fitted at overparameterization.
Gradient estimates for nonlinear parabolic equations on metric spaces.
problem Nonexistence of positive solutions to nonlinear parabolic equations.
method Local elliptic and parabolic gradient estimates.
result Conditions guaranteeing the nonexistence of nontrivial positive solutions.
The paper derives new gradient and Hessian estimates for nonlinear parabolic equations.
problem Estimating solutions to nonlinear weighted parabolic equations.
method Derives Li-Yau and Hamilton type gradient estimates, and Hessian estimates.
result New gradient and Hessian estimates for positive solutions of nonlinear parabolic equations.
Convex program for estimating nonlinear recurrent models with stability conditions.
problem Estimating parameters in nonlinear recurrent models with stability conditions.
method Formulated a convex program for the estimator of nonlinear recurrent models under stability conditions.
result Sample complexity for the convex program estimator under stable dynamics.
We introduce a data-based approach to estimating key quantities which arise in the study of nonlinear control systems and random nonlinear dynamical systems. Our approach hinges on the observation that much of the existing linear theory may be readily extended to nonlinear systems - with a reasonable expectation of suc…
Estimates input from output of nonlinear systems using ANN.
problem Estimating unknown compositional input from system output.
method Artificial Neural Networks (ANNs) for nonlinear system inversion.
result ANNs can compete with optimal bounds for linear systems and demonstrate promising results for nonlinear systems.
The paper provides gradient estimates for nonlinear heat-type equations on smooth metric measure spaces.
problem Proving gradient estimates for nonlinear heat-type equations on smooth metric measure spaces.
method Using Hamilton type and Li-Yau type estimates, the paper proves gradient estimates on positive solutions to generalized nonlinear parabolic equations on smooth metric measure spaces with compact boundary.
result Gradient estimates for nonlinear heat-type equations on smooth metric measure spaces.
Estimates derived for solutions of Neumann problems on Riemannian manifolds.
problem Gradient and second order estimates for solutions of fully nonlinear elliptic equations on compact Riemannian manifolds.
method Derivation of gradient and second order {\em a priori} estimates.
result Existence and regularity results for solutions of Neumann problems.
The paper proves gradient estimates for nonlinear parabolic equations on smooth metric measure spaces.
problem Proving gradient estimates for nonlinear parabolic equations on smooth metric measure spaces.
method Using Souplet-Zhang type estimates and properties of Bakry-Emery Ricci tensor and weighted mean curvature.
result Gradient estimates for nonlinear parabolic equations on smooth metric measure spaces with Dirichlet boundary condition.
The paper provides gradient estimates for solutions to nonlinear parabolic equations under Ricci flow.
problem Gradient estimates for positive solutions to nonlinear parabolic equations under Ricci flow.
method Maximum principle and cutoff function approach.
result Gradient estimates and Harnack inequalities for positive solutions to the heat equation under Ricci flow.
Paper develops a new state estimation method for nonlinear systems.
problem State estimation for nonlinear state-space models is intractable.
method Developed a variational inference approach based on Gaussian approximations.
result The method outperforms alternative Gaussian approaches in various examples.
The paper analyzes parameter estimation from nonlinear observations.
problem Recovering a structured but unknown parameter from nonlinear observations.
method Develops a framework for characterizing time-data tradeoffs for various parameter estimation algorithms.
result Projected gradient descent schemes converge at a linear rate with near minimal number of samples.
Method estimates parameters of complex nonlinear systems.
problem Parameter estimation for nonlinear systems with derivative states.
method Regularized linear regression using differentiation filtering and least squares.
result Finite-sample bound on mean absolute error of estimation.
Sharp inscribed radius estimate for curved surfaces.
problem Estimating the inscribed radius of curved surfaces.
method Proving a sharp estimate for inscribed radius under fully nonlinear curvature flows.
result The estimate is asymptotically sharp on cylinders.
Projected Gradient Descent Algorithms for Solving Nonlinear Inverse Problems with Generative Priorsstat.ML
PGD algorithms solve nonlinear inverse problems with generative priors using noisy measurements.
problem Signal estimation from noisy nonlinear measurements with generative priors.
method Projected gradient descent algorithms for two cases: unknown and known nonlinearity.
result PGD algorithms converge linearly to optimal statistical rates using arbitrary initialization.
Paper proves rigidity estimates for hyperbolic shells and applies them to \(Γ\)-limit theory.
problem Rigidity of hyperbolic shells and their \(Γ\)-limit behavior.
method Nonlinear rigidity estimates for \(H^1\) deformations and hyperbolic shells with clamped lateral boundary.
result Derives the optimal exponent \(h^{-4/3}\) for hyperbolic shells.
The paper proves estimates for solutions to nonlinear equations on manifolds with boundary.
problem Boundary estimates for fully nonlinear Yamabe equations on Riemannian manifolds.
method Deriving a priori second derivative estimates for subsolutions.
result Existence of smooth solutions with uniform estimates.
Data-Efficient Non-Gaussian Semi-Nonparametric Density Estimation for Nonlinear Dynamical Systemsmath.OC
This paper presents a method for efficient density estimation in nonlinear systems.
problem Accurate representation of non-Gaussian distributions in nonlinear dynamical systems is challenging.
method Uses Seminonparametric (SNP) densities with probabilists' Hermite polynomial basis and Monte Carlo approximation for maximum likelihood estimation.
result Demonstrates that the method can accurately capture non-Gaussian density structure and compute quantiles using fewer samples than raw Monte Carlo.
Subgradient estimates for a nonlinear subparablic equation on complete pseudo-Hermitian manifoldsmath.DG
The paper derives subgradient estimates for a specific nonlinear subparabolic equation on pseudo-Hermitian manifolds.
problem Deriving subgradient estimates for positive solutions to a nonlinear subparabolic equation on pseudo-Hermitian manifolds.
method Using the CR sub-Laplacian comparison property, the paper derives local subgradient estimates for positive solutions to the given equation.
result The paper establishes subgradient estimates for positive solutions to the nonlinear subparabolic equation.
Local gradient estimates of solutions to some conformally invariant fully nonlinear equationsmath.AP
This paper concerns local gradient estimates to solutions of general conformally invariant fully nonlinear elliptic equations of second order.
Solves Dirichlet problem for fully nonlinear equations on Hermitian manifolds.
problem Solving Dirichlet problem for fully nonlinear equations on Hermitian manifolds.
method Derived estimates and gradient estimates for solutions.
result Solved Dirichlet problem with admissible subsolutions in some cases.
The paper provides new gradient estimates for solutions to a nonlinear elliptic equation on smooth metric measure spaces.
problem Gradient estimates for solutions to a specific nonlinear elliptic equation on smooth metric measure spaces.
method Nash-Moser iteration technique to obtain local gradient estimates.
result New local gradient estimates for positive solutions to the equation.
The paper studies fully nonlinear equations on Hermitian manifolds, proving existence and interior estimates.
problem Proving existence and interior estimates for fully nonlinear equations on Hermitian manifolds.
method Derives interior estimates and establishes the existence of smooth solutions for the Dirichlet problem and equations on closed manifolds.
result Derives interior estimates and establishes the existence of smooth solutions for the Dirichlet problem and equations on closed manifolds.
Gradient estimates for the nonlinear parabolic equation with two exponents on Riemannian manifoldsmath.DG
Study gradient estimates for nonlinear parabolic equations on Riemannian manifolds.
problem Estimating gradients for nonlinear parabolic equations on Riemannian manifolds.
method Analyzes Fisher-KPP, parabolic Allen-Cahn, and Newell-Whitehead equations on complete noncompact Riemannian manifolds.
result Gradient estimates for positive solutions and Liouville theorem for ancient solutions.
The paper deals with incorporating statistical uncertainty in decision-making.
problem Statistical uncertainty in decision-making.
method Theory of nonlinear expectations.
result Explicit and consistent incorporation of uncertainty in decision valuation.
We present a method to derive local estimates for some classes of fully nonlinear elliptic equations. The advantage of our method is that we derive Hessian estimates directly from estimates. Also, the method is flexible and can be applied to a large class of equations.
Paper uses variational inference to estimate nonlinear models.
problem Parameter estimation for nonlinear state-space models.
method Variational inference approach for nonlinear state-space models.
result The method provides robust parameter estimates and outperforms alternatives.
The study proves estimates for transverse nonlinear equations on Sasakian manifolds with applications in geometry.
problem Estimating transverse fully nonlinear equations on Sasakian manifolds.
method Proving a priori estimates for transverse fully nonlinear equations.
result The study proves estimates for transverse fully nonlinear equations on Sasakian manifolds and gives geometric applications.
Estimates and Existence Results for a Fully Nonlinear Yamabe Problem on Manifolds with Boundarymath.AP
This paper concerns a fully nonlinear version of the Yamabe problem on manifolds with boundary. We establish some existence results and estimates of solutions.
Proposes an INLA-based method for state and parameter estimation in nonlinear systems.
problem Difficulty in learning parameters accurately in nonlinear dynamical systems.
method Iterated INLA for state and parameter estimation in nonlinear dynamical systems.
result Outperforms existing methods on data assimilation tasks.
Estimates for complex equations on manifolds derived from a conjecture.
problem Estimating solutions to complex equations on Hermitian manifolds.
method Developed second order estimates for fully nonlinear elliptic equations with gradient terms.
result Derived global estimates for an equation related to Gauduchon's conjecture.
Uniform estimates for complex equations on compact manifolds found.
problem Uniform estimates for form fully nonlinear PDEs on compact Hermitian manifolds.
method Local comparison with Monge-Ampère equations and finding an appropriate elliptic operator.
result A priori estimate for the equations.
A Family of Computationally Efficient and Simple Estimators for Unnormalized Statistical Modelscs.LG
We introduce a new family of estimators for unnormalized statistical models. Our family of estimators is parameterized by two nonlinear functions and uses a single sample from an auxiliary distribution, generalizing Maximum Likelihood Monte Carlo estimation of Geyer and Thompson (1992). The family is such that we can e…
Proposes KAR for nonlinear causal discovery using kernel methods.
problem Learning causal relationships in nonlinear settings.
method Kernel anchor regression (KAR) with improved three-stage nonparametric regression.
result KAR outperforms existing methods in nonlinear causal discovery.
Elliptic gradient estimates and Liouville theorems for a weighted nonlinear parabolic equationmath.DG
The paper derives estimates and proves theorems for a specific type of nonlinear parabolic equation.
problem Analyzing solutions to a weighted nonlinear parabolic equation on metric measure spaces.
method Derives elliptic gradient estimates and proves Liouville-type theorems.
result Establishes conditions for the existence of positive ancient solutions.
Optimizes sparse signal recovery using nonlinear approximations.
problem Recovering sparse stochastic signals efficiently.
method Probabilistic approach with linear and nonlinear estimators.
result Structured estimator outperforms linear in MSE.
Bayesian method improves predictions in overparameterized nonlinear regression.
problem Understanding overparameterization in nonlinear regression models.
method Bayesian framework with adaptive prior considering data spectral structure.
result Posterior contraction established for generalized linear and single-neuron models, demonstrating prediction consistency.
Active learning method estimates nonlinear systems efficiently.
problem Identifying nonlinear dynamical systems with continuous states and actions.
method Repeating three steps: trajectory planning, tracking, and re-estimation.
result Estimates nonlinear dynamical systems at a parametric rate.
The paper tackles matrix completion under nonlinear distortions.
problem Matrix completion with nonlinear distortions.
method Alternates between low-rank matrix estimation and monotonic function estimation.
result Empirical results show the method's competitiveness.
Improved RBFNN for nonlinear system identification.
problem Nonlinear system identification problem.
method Spatio-temporal extension of RBFNN with time-space orthogonality.
result Spatio-temporal RBFNN outperforms standard RBFNN in convergence and error reduction.