The class of non-rigid registration methods proposed in the framework of PDE-constrained Large Deformation Diffeomorphic Metric Mapping is a particularly interesting family of physically meaningful diffeomorphic registration methods. PDE-constrained LDDMM methods are formulated as constrained variational problems, wher…
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.
168,657 papers · 148 categories
Trend · papers per month
29 results for “PDE-constrained”
Study uses outer metrics for PDE-constrained shape optimization over diffeomorphism group.
problem Optimizing shapes governed by PDEs over the diffeomorphism group.
method Outer metrics on diffeomorphism group, Riemannian steepest descent method.
result Riemannian approach outperforms other metrics in solving PDE-constrained shape optimization problems.
Functional-prior-based approaches to Bayesian PDE-constrained inversion using physics-informed neural networksphysics.geo-ph
Unified framework for Bayesian PDE-constrained inversion using physics-informed neural networks.
problem Incorporating prior distributions in function space into Bayesian PINN-based inversion.
method Functional-prior-based approaches (fpBPINN) to Bayesian PDE-constrained inversion using physics-informed neural networks (PINNs). Two complementary approaches: FPI-BPINN and fParVI-PINN.
result Accurate estimation of posterior distributions in seismic traveltime tomography and Darcy-flow permeability inversion.
PDE-DKL combines NNs and GPs for high-dimensional PDE problems.
problem High-dimensional PDE problems with scarce data.
method PDE-constrained Deep Kernel Learning (PDE-DKL) framework.
result High accuracy with reduced data requirements.
Optimal neural network approximation for Wasserstein gradient direction via convex optimization.
problem Approximating Wasserstein gradient direction with limited data.
method Two-layer networks with squared-ReLU activations, SDP relaxation.
result Optimal approximation of Wasserstein gradient direction in two-layer networks.
Stochastic optimization is key to efficient inversion in PDE-constrained optimization. Using 'simultaneous shots', or random superposition of source terms, works very well in simple acquisition geometries where all sources see all receivers, but this rarely occurs in practice. We develop an approach that interpolates d…
New method solves constrained optimization problems efficiently.
problem Equality-constrained nonlinear, nonconvex optimization problems.
method Adaptive inexact Newton method with randomized iterative sketching.
result Global almost sure convergence and local linear/superlinear convergence.
Diffeologies unify infinite-dimensional geometry and PDEs, enhancing classical function spaces.
problem Combining infinite-dimensional geometry and PDEs for optimization problems.
method Review and extension of classical function spaces and mapping spaces.
result Diffeologies provide a unified framework for evolution equations and optimization problems.
Space mapping speeds up shape optimization for PDEs.
problem Efficiently solving shape optimization problems constrained by PDEs.
method Combines fine and coarse model optimizations using Riemannian metrics.
result Space mapping methods are highly efficient for complex shape optimization problems.
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.
We find ways to make physical signals misclassified by computer vision models.
problem Vulnerability of signal classifiers to adversarial perturbations in physical signals.
method Solving PDE-constrained optimization problems to construct imperceptible perturbations.
result Effective and physically realizable adversarial perturbations can be computed for machine learning models.
NWoS solves high-dimensional Poisson equations using neural networks.
problem Efficiently solving high-dimensional Poisson equations.
method Neural Walk-on-Spheres (NWoS) leveraging stochastic representations and Walk-on-Spheres methods.
result NWoS outperforms competing methods in accuracy, speed, and computational costs.
Gradient-free framework for Bayesian experimental design in complex systems.
problem Optimal experimental design in systems where gradient information is unavailable.
method Combines EKI and ALDI for optimization and sampling, with approximations for scalable utility estimation.
result Demonstrates robust, accurate, and efficient experimental design in various complex systems.
Stochastic seismic waveform inversion using generative adversarial networks as a geological priorphysics.geo-ph
We present an application of deep generative models in the context of partial-differential equation (PDE) constrained inverse problems. We combine a generative adversarial network (GAN) representing an a priori model that creates subsurface geological structures and their petrophysical properties, with the numerical so…
New methods for Bayesian inference using mean shift particle systems.
problem Approximating expectations with unnormalized densities in Bayesian inference.
method Mean shift interacting particle systems that minimize maximum mean discrepancy (MMD).
result Mean shift interacting particle systems converge quickly and capture complex distributions.
GeoFunFlow: Geometric Function Flow Matching for Inverse Operator Learning over Complex Geometriescs.LG
GeoFunFlow tackles inverse problems on complex geometries with efficient learning.
problem Challenges in inverse problems governed by PDEs, especially on irregular geometries.
method Combines geometric function autoencoder and latent diffusion model trained via rectified flow.
result Achieves state-of-the-art reconstruction accuracy and efficient inference.
This paper extends the Risk Quadrangle framework for risk management and optimization.
problem Integrating risk management, optimization, and statistical estimation.
method Review and extension of the Risk Quadrangle framework with new quadrangles.
result New quadrangles offer novel approaches to risk-sensitive decision-making.
Bayesian Gaussian process models handle uncertain data locations in PDE approximations.
problem Handling uncertainties in data locations for PDE approximations.
method Bayesian inference of uncertain inputs integrated into Gaussian process predictions.
result Substantial reduction in predictive uncertainties achieved through Bayesian inference.
Space mapping calibrates financial models, shown feasible for Heston model.
problem Calibrating financial models with few observable parameters and non-linear constraints.
method Space mapping approach using a coarse surrogate model and fine model calibration.
result Space mapping approach feasible for Heston model calibration.
Extends dimension reduction to data-driven settings without gradients.
problem Gradient-based dimension reduction limitations in data-driven settings.
method Score ratio matching framework, tailored parameterization, regularization, eigenvalue deflation.
result Outperforms standard score-matching for problems with low-dimensional structure.
In many hierarchical inverse problems, not only do we want to estimate high- or infinite-dimensional model parameters in the parameter-to-observable maps, but we also have to estimate hyperparameters that represent critical assumptions in the statistical and mathematical modeling processes. As a joint effect of high-di…
Efficiently optimizes hyperparameters for PDE and inverse problems using Gaussian processes.
problem Hyperparameter optimization for scientific computing and inference methods.
method Bilevel optimization with Gauss-Newton linearization for efficient hyperparameter updates.
result Significant improvements in accuracy and robustness compared to random initialization.
Deep learning observables in computational fluid dynamicsphysics.comp-ph
Many large scale problems in computational fluid dynamics such as uncertainty quantification, Bayesian inversion, data assimilation and PDE constrained optimization are considered very challenging computationally as they require a large number of expensive (forward) numerical solutions of the corresponding PDEs. We pro…
Estimates expected information gain using density approximations and dimension reduction.
problem Estimating expected information gain in nonlinear and non-Gaussian settings.
method Flexible transport-based schemes for EIG estimation, optimal sample allocation, and gradient-based upper bounds on mutual information.
result Optimal sample allocation and dimension reduction schemes improve EIG estimation accuracy and convergence rate.
Accelerating PDE-constrained Inverse Solutions with Deep Learning and Reduced Order Modelsphysics.comp-ph
Inverse problems are pervasive mathematical methods in inferring knowledge from observational and experimental data by leveraging simulations and models. Unlike direct inference methods, inverse problem approaches typically require many forward model solves usually governed by Partial Differential Equations (PDEs). Thi…
A new MCMC method combines low and high-fidelity models to reduce computation.
problem Inefficient computation of expensive target densities in scientific applications.
method Pseudo-marginal MCMC approach using a telescoping series of low-fidelity models.
result Asymptotically exact multi-fidelity MCMC algorithms for reduced computational cost.
LPINNs solve complex PDEs by reformulating PINNs on Lagrangian frame, reducing training complexity.
problem Complexity in training PINNs, especially for convection-diffusion equations.
method Propose LPINNs, a Lagrangian reformulation of PINNs, with two branches solving state variables and characteristics curves.
result Loss landscapes of LPINNs are less sensitive to problem complexity compared to traditional PINNs.
PDEs constrain smooth functions in neural networks.
problem Understanding functions computable by neural networks.
method Analyzing smooth hierarchical functions via PDEs.
result Established algebraic PDEs for smooth functions.
A new method lifts training of input-convex neural networks to avoid dead weights and plateaued loss.
problem Training input-convex neural networks with non-negative weights.
method Introduces a hypernetwork that emits non-negative weights from a summary of the input batch, adding stochasticity to soften the loss landscape.
result The lift method achieves lower test loss than projected gradient descent and direct softplus reparametrization.