Modeling bone microarchitecture adaptation using geometric flows.
problem Bone microarchitecture adaptation modeling.
method Advection and mean curvature flow model with a sphere as a test case.
result Closed-form solution for sphere under advection and mean curvature flow.
We study \emph{TV regularization}, a widely used technique for eliciting structured sparsity. In particular, we propose efficient algorithms for computing prox-operators for ℓp-norm TV. The most important among these is ℓ1-norm TV, for whose prox-operator we present a new geometric analysis which unveils a …
A new model explains how people solve physical problems and judge hand usage.
problem Understanding how people solve physical problems and judge hand usage.
method Developed a model that plans over symbolic representation, uses geometric solver, and checks feasibility with physical constraints.
result Model explains participants' actions and judgments with high quantitative accuracy.
A neural atlas simplifies 3D geometry simulation by avoiding meshing.
problem Simulation of complex 3D geometries with thin features or non-trivial topology.
method Learned geometric representation of overlapping volumetric coordinate charts, trained from point-cloud or level-set data.
result The learned atlas enables different solvers without re-meshing or re-parametrization.
Exact solver speeds up Weston-Watkins SVM subproblem significantly.
problem Improving performance of Weston-Watkins multiclass SVM.
method Novel reparametrization for exact subproblem solving.
result Significant speed-up over state-of-the-art solvers for large number of classes.
Proposes a new regularizer for semi-supervised learning on multilayer graphs.
problem Semi-supervised learning on multilayer graphs with labeled and unlabeled data.
method Generalized matrix mean regularizer and matrix-free numerical scheme.
result The regularizer outperforms state-of-the-art methods numerically.
Optimizes neural networks with blackbox solvers using Time-cost Regularization.
problem Improving neural network performance by integrating efficient solvers for complex problems.
method Optimizes both the primary loss function and the performance of the blackbox solver using Time-cost Regularization. Introduces a hyper-blackbox concept to learn blackbox parameters.
result Significant improvement in neural network performance through optimization of blackbox solvers.
Study analyzes 3,171 stocks to pick efficient portfolios using quantum and classical solvers.
problem Creating efficient stock portfolios from a large dataset.
method Used classical and quantum solvers to optimize portfolios of 3,171 US stocks.
result Demonstrated the effectiveness of quantum and classical solvers in portfolio optimization.
A practical algorithm improves approximate OT distances using quantization.
problem Substantial computational burden in computing OT distances for large samples.
method Introduces a quantization step to estimate OT distances between measures.
result The quantization step improves the performance of approximate solvers for entropy-regularized transport.
The paper speeds up hyperparameter optimisation in Gaussian processes.
problem Scaling hyperparameter optimisation to large datasets.
method Improvements to linear system solvers (pathwise gradient, warm starting, early stopping).
result Speed-ups of up to 72x and residual norm decreases of up to 7x.
New solver MPLP++ outperforms existing solvers for dense graph models.
problem Efficiently solving dense, discrete Graphical Models with pairwise potentials.
method Dual Block-Coordinate Ascent with MPLP++ modification.
result MPLP++ significantly outperforms existing solvers, including TRWS.
GENO framework generates efficient solvers for machine learning problems.
problem Designing efficient solvers for machine learning problems.
method GENO framework combines a modeling language with a generic solver to generate solvers from optimization problem specifications.
result Automatically generated solvers are as efficient as well-engineered specialized solvers and orders of magnitude more efficient than classical modeling language plus solver approaches.
Neural network learns fast PDE solvers with proven guarantees.
problem Designing fast iterative solvers for specific PDE problems.
method Learn to modify an existing solver using a deep neural network.
result Achieves 2-3 times speedup compared to state-of-the-art solvers.
CRA improves UL-based CO solvers by dynamically smoothing and enforcing discreteness.
problem Local optima and artificial rounding issues in UL-based CO solvers.
method Continuous Relaxation Annealing (CRA) strategy that dynamically shifts from continuous to discrete solutions.
result Significantly enhances UL-based CO solver performance and eliminates artificial rounding.
Study compares 5 ODE solvers on 3 case studies, finding varying accuracy.
problem Comparing estimation accuracy of 5 ODE solvers on 3 case studies.
method Used 5 different numerical ODE solvers (Euler's, Heun's, Midpoint, Runge-Kutta 4th order, ODE45) on 3 case studies and compared their results.
result Different solvers have varying accuracy depending on the case study.
A new method combines classical and machine learning PDE solvers efficiently.
problem Combining classical and machine learning PDE solvers to reduce computational cost and improve accuracy.
method Proposes an approximate greedy router to select solvers at each iteration, mimicking a greedy approach.
result Consistently reduces final error and AUC of the error trajectory compared to single-solver baselines and hybrid approaches.
Higher-order ODE solvers improve deep learning performance.
problem Improving deep learning performance using higher-order ODE solvers.
method Evaluation and improvement of Runge-Kutta (RK) methods for deep learning.
result Higher-order RK solvers can improve deep learning performance by incorporating key ingredients of optimizers.
SA-Solver improves stochastic sampling from DPMs.
problem Efficient sampling from Diffusion Probabilistic Models (DPMs) is time-consuming.
method Proposes SA-Solver, an improved stochastic Adams method for solving diffusion SDE.
result SA-Solver achieves improved or comparable performance compared to SOTA methods for few-step sampling.
Accelerates data generation in score-based models.
problem Slow generation of realistic data by score-based models.
method Developed an adaptive step size SDE solver.
result Generates data 2-10 times faster with high quality.
New deep learning solver for high-dimensional derivative pricing.
problem High-dimensional derivatives pricing problems.
method Combines deep learning with least square regression for backward SDE solving.
result Accurate and efficient pricing of complex derivatives.
New taxonomy and improved solvers for discrete energy minimization.
problem Maximum-a-posteriori inference in discrete graphical models.
method Dual block-coordinate ascent rule, theoretical analysis, new solver variants.
result Improved state-of-the-art solver outperforming existing methods on all test instances.
End-to-end trainable graph matching using improved combinatorial solvers.
problem Graph matching in deep learning.
method Combining deep learning with optimized combinatorial solvers.
result Advances state-of-the-art on deep graph matching benchmarks.
MIP-GNN uses graph neural networks to predict variable biases for MIP solvers.
problem Improving combinatorial optimization through data-driven insights.
method Encoding MILP interactions as graphs, training a graph neural network to predict variable biases, and guiding the MIP solver with these predictions.
result Significant improvements in solving binary MILPs compared to default settings of state-of-the-art solvers.
Developing stable and scalable probabilistic ODE solvers for stiff and high-dimensional problems.
problem Stiff and high-dimensional ODEs
method Matrix-free update step and iterative re-linearization
result Improved stability and scalability
DPM-Solver speeds up DPM sampling to 10-20 function evaluations.
problem Slow sampling from Diffusion Probabilistic Models (DPMs).
method Exact formulation of diffusion ODE solutions, using change-of-variable and exponentially weighted integral.
result Generates high-quality samples in 10-20 function evaluations.
The paper improves ODE solvers by integrating diverse information types.
problem Improving accuracy and physical meaningfulness of ODE solutions.
method Leveraging probabilistic solvers to include second-order information and physical conservation laws.
result Solutions become more accurate and physically meaningful with additional information.
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.
Ada-LISTA adapts neural solvers for varying models.
problem Adapting neural solvers for varying models.
method Ada-LISTA receives pairs of signals and dictionaries, learns a universal architecture, and solves sparse coding in linear rate.
result Ada-LISTA solves sparse coding in linear rate for varying models.
ML4CO uses machine learning to improve combinatorial optimization solvers.
problem Solving combinatorial problems in practice often involves related data distributions.
method Replacing heuristic components with machine learning approaches.
result Improved state-of-the-art combinatorial optimization solvers.
New ODE solvers improve training efficiency and accuracy.
problem Training Neural ODEs requires efficient and accurate gradient calculation.
method Presented algebraically reversible ODE solvers that are time and memory efficient, calculate exact gradients, and are numerically stable.
result Reversible solvers strictly improve upon previous architectures in efficiency and accuracy.
GENIE accelerates DDM synthesis with higher-order solvers.
problem Efficiently solving the differential equation for high-quality generation.
method Higher-order Taylor methods, utilizing Jacobian-vector products.
result GENIE significantly accelerates synthesis compared to previous solvers.
New solver avoids memory issues for long differential equations.
problem Memory constraints in adaptive probabilistic ODE solvers.
method Fixed memory demands adaptive probabilistic solver using robust state estimation.
result Eliminates memory issues for long time series simulations.
skscope simplifies sparsity-constrained optimization in Python.
problem Tedious mathematical deduction and programming for sparsity-constrained optimization.
method Introduces skscope, a Python library that allows users to solve sparsity-constrained optimization problems by just programming the objective function.
result skscope enables state-of-the-art solvers to quickly attain sparse solutions in high-dimensional spaces, achieving up to 80x speedup.
C-ADAM is a new adaptive solver for complex nested problems.
problem Solving compositional problems involving nested expected values.
method Adaptive solver for non-linear functional nesting of expected values.
result C-ADAM converges to a stationary point in O(δ−2.25). Novel probabilistic solver speeds up solving related linear systems.
problem Efficiently solving multiple related linear systems.
method Probabilistic linear solver over the parameter space, leveraging solved systems.
result Faster and more efficient solution of related linear systems.
This work introduces a new loss function to improve the efficiency of optimization-based PDE solvers.
problem Optimization-based PDE solvers converge slowly and are inefficient compared to classical iterative solvers.
method Proposes a novel Stabilized Gradient Residual (SGR) loss function to modulate the condition number.
result The SGR loss achieves orders-of-magnitude faster convergence than the MSE loss in both ODIL and PINNs frameworks.
Machine learning speeds up GPR simulations.
problem Computational demands of simulating practical GPR problems.
method Automatic ML-based forward solver framework using gprMax.
result Near-real-time GPR simulations achieved.
Paper accelerates linear programming by two orders of magnitude.
problem Efficiently solving large linear programming problems with limited data.
method Parallelizable acceleration framework for packing linear programs.
result Framework provides approximately optimal solutions with significant speedup.
ThiopheneIV is a new solver for implied volatility with proven monotonicity.
problem Efficiently solving implied volatility in financial models.
method Monotone core with Euler-Chebyshev and Halley steps, exact arithmetic proof, practical boundary handling.
result ThiopheneIV agrees closely with multiprecision Black reference prices at low latency.
PDE-based G-CNNs add geometric symmetries to CNNs without augmentation.
problem Designing CNNs with built-in symmetries like rotation.
method Formulate CNN layers as PDE solvers on homogeneous spaces.
result PDE-G-CNNs achieve better performance with fewer parameters.
New framework for probabilistic linear solvers reduces manual effort.
problem Manual implementation of probabilistic iterative methods is laborious.
method Affine Tracing: Automatically constructs PIMs from standard implementations.
result Any realistic affine PIM is calibrated, motivating their adoption.
Paper tackles conditional learning between different domains.
problem Learning conditional distribution between input and output domains.
method Cooperative training of fast and slow thinking models.
result Jointly trained models improve conditional learning tasks.
Study uses machine learning to recommend best solvers for slab transport problems.
problem Auto-selecting the best solvers for transport problems in uniform slabs.
method Three solvers (Richardson, diffusion synthetic acceleration, nonlinear diffusion acceleration) and five machine learning algorithms (linear discriminant analysis, K-nearest neighbors, support vector machine, random forest, neural networks) were tested.
result Random forest and K-nearest neighbors showed potential as best solvers for classification problems.
LeapsAndBounds configures solvers efficiently for unknown problem distributions.
problem Configuring general-purpose solvers to run efficiently on unknown problem instances.
method LeapsAndBounds tests configurations on randomly selected problem instances for longer and longer time.
result LeapsAndBounds achieves a runtime close to the optimal expected runtime with near-optimal running time.
Study evaluates Deep PDE solvers for high-dimensional option pricing, identifying key sources of error.
problem Empirical study on error analysis of Deep PDE solvers for high-dimensional option pricing.
method Comparative experiments with Deep BSDE method and other solvers, identifying three main sources of error.
result Deep BSDE method is superior and robust to option specifications, improving with larger batch sizes and fewer time steps.
Calibrated probabilistic solvers improve accuracy of ODE estimates.
problem Uncertainty in probabilistic ODE solutions is not well-calibrated for adaptive step sizes.
method Introduce and assess several calibration methods for probabilistic ODE solvers.
result Calibration methods interact efficiently with adaptive step-size selection, improving posteriors.
New method combines QQA and gradient-based sampling for combinatorial optimization.
problem Scalability challenges in learning-based solvers for combinatorial optimization.
method Integrates gradient-based update through continuous relaxation with Quasi-Quantum Annealing (QQA) and parallel communication.
result Achieves superior speed-quality trade-offs for large-scale instances.
SATNet integrates logical reasoning into deep learning with a differentiable MAXSAT solver.
problem Integrating logical reasoning into deep learning architectures.
method Differentiable MAXSAT solver based on fast coordinate descent for SDP.
result Minimally supervised learning of logical structures in deep learning systems.