Optimizes PDE-constrained LDDMM for efficient non-rigid registration.
problem Inexact Newton-Krylov optimization in PDE-constrained LDDMM leads to poor geodesic paths.
method Band-limited vector field parameterization to optimize computational complexity.
result Optimized method shows competitive performance with reduced memory load and computational time.
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.
Develops a method to interpolate data for efficient inversion in nonuniform geometries.
problem Efficient inversion in nonuniform geometries where not all sources see all receivers.
method Interpolates data to an ideal acquisition geometry while solving the inverse problem using simultaneous shots.
result Illustrates the flexibility and efficiency of the approach using synthetic experiments.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
New methods tackle complex inverse problems with scalable optimization-based MCMC.
problem Estimating high-dimensional model parameters and hyperparameters in nonlinear hierarchical statistical inverse problems.
method Optimization-based Markov chain Monte Carlo (MCMC) methods using RTO and pseudo-marginal MCMC.
result Efficient sampling tools for hierarchical Bayesian inversion with robust performance to model parameter dimensions.
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.
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.
Deep learning predicts fluid dynamics parameters from few samples.
problem Challenging computational fluid dynamics problems requiring many expensive PDE solutions.
method Deep artificial neural networks trained on a few samples to predict input parameters to observable.
result Robust and efficient neural network approximations of parameters to observable map, with low prediction errors and computational savings.
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.
Generative models improve seismic wave inversion for subsurface structure.
problem Inaccurate subsurface geological structures in seismic inversion.
method Combining GAN for geological priors with PDE solution for wave propagation, using approximate MALA sampling.
result Efficient Bayesian inversion yields diverse realizations of subsurface structures matching seismic observations.
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.
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.
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.
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.
This paper accelerates inverse solutions for PDEs using ML and ROMs.
problem Efficiently solving inverse problems governed by PDEs with many forward model solves.
method Combining ML with ROMs to improve accuracy and speed.
result ML-enhanced ROMs accelerate inverse problem solving.
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.
Bayesian optimization reduces computational effort in aircraft design optimization.
problem High computational cost in industrial aircraft design optimization.
method Constrained Bayesian optimization (Super Efficient Global Optimization with Mixture of Experts)
result Significant computational efficiency improvements over existing Isight optimizers.
New model reduces hyperparameter optimization time and improves transfer learning.
problem Hyperparameter optimization for machine learning across multiple datasets.
method Developed a new ensemble model for Bayesian optimization that transfers knowledge between datasets.
result Substantially reduces optimization time and improves over state-of-the-art transfer hyperparameter optimization.
Bayesian optimization outperforms other methods in nano-optical shape optimization and parameter reconstruction.
problem Optimizing nano-optical structures with non-convex objective functions.
method Benchmarked five global optimization methods including Bayesian optimization.
result Bayesian optimization yields significantly better results in a fraction of the time.
Bayesian optimization method tackles combinatorial spaces, scalable for large data.
problem Optimization over combinatorial categorical spaces in natural sciences.
method Combines variational optimization and continuous relaxations for gradient-based optimization.
result Method performs comparably to state-of-the-art methods while scaling well.
New algorithm solves complex stopping problems with robust optimization.
problem Solving complex stochastic optimal stopping problems.
method Simulation-based robust optimization with exact reformulation as a zero-one bilinear program.
result Developed polynomial-time heuristics and algorithms for practical solution.
L2O uses ML to optimize traditional optimization techniques.
problem Real-world optimization problems with shared structures.
method Exploiting shared structures to enhance optimization techniques.
result Better or faster solutions through machine learning integration.
BLOSSOM optimizes switching between local and Bayesian methods for faster convergence.
problem Optimizing function evaluations efficiently and converging to global minimum.
method Combines local and Bayesian optimization with a stopping condition based on expected regret.
result Achieves superior convergence and efficient use of function evaluations.
Survey of DRO, a robust optimization framework.
problem Risk-aversion and chance-constrained optimization challenges.
method Distributionally robust optimization (DRO) framework.
result DRO's growing importance in operations research and statistics.
A novel neural network approach for optimization problems.
problem Constrained optimization problems.
method Neural Optimization Machine (NOM) using a specially designed NN architecture and training procedure.
result Solves optimization problems efficiently, especially in high-dimensional spaces.
Meta algorithm solves multivariate optimization using univariate optimizers.
problem Multivariate global optimization problems.
method Meta algorithm combining univariate global optimizers.
result Meta algorithm provides robust regret guarantees.
New algorithms ensure reproducibility and optimal convergence in convex optimization.
problem Trade-off between reproducibility and convergence rate in convex optimization.
method Regularization-based algorithms for smooth convex minimization and minimax optimization.
result Achieves optimal reproducibility and near-optimal gradient complexity for various oracle settings.
Proposes deep optimal feedback control for continuous-time systems with action constraints.
problem Learning optimal feedback control laws for robotic applications.
method Exploits Hamilton-Jacobi-Bellman equation and deep differential networks to learn optimal value function and feedback policy.
result Enables learning an optimal feedback control law that generates an optimal trajectory from any point in state-space without replanning.
New algorithm selects robust martingale for optimal stopping problems.
problem Optimal stopping problems in stochastic processes.
method Randomized dual martingale minimization algorithm.
result Efficiently selects Doob martingale as close as possible.
Optimizes stochastic and online optimization methods based on problem geometry.
problem Optimizing computational and statistical outcomes in stochastic and online optimization problems.
method Characterizes optimal methods based on constraint set and gradient geometry.
result Stochastic and adaptive-gradient methods are optimal for quadratically convex constraint sets.
Optimizes K-means clustering with PSO for better accuracy.
problem Improving the accuracy of K-means clustering.
method Uses Particle Swarm Optimization (PSO) to find optimal initial centroids for K-means.
result Optimal centroids found using PSO lead to better clustering accuracy.
Topological Bayesian Optimization finds optimal structures using topological data.
problem Optimizing complex structured data like material or neural network structures.
method Extract topological information from structures using persistent homology, apply Bayesian optimization with kernels for persistence diagrams.
result Topological information improves search efficiency for optimal structures.
This paper shows how to combine optimal tests into log-optimal processes.
problem How to combine optimal sequential tests into log-optimal processes.
method Using a new class of WAIT e-processes, the paper aggregates asymptotically optimal sequential tests into asymptotically log-optimal processes.
result It is possible to aggregate asymptotically optimal sequential tests into asymptotically log-optimal e-processes.
New algorithm AG-OG optimizes separable convex-concave problems efficiently.
problem Efficiently solving separable convex-concave minimax optimization problems.
method Leverages Nesterov acceleration and optimistic gradient on component and coupling parts of the problem.
result Achieves optimal convergence rate for various settings including bilinearly coupled problems.
Adapts Bayesian optimization for mixed constraints in aircraft design.
problem Optimizing expensive black box functions with mixed constraints.
method Super efficient global optimization with upper trust bound for constraints, Gaussian process uncertainty, refinement procedure.
result Superior performance on aircraft design problem compared to state-of-the-art solvers.