Deep learning method improves numerical approximation of FBSDEs with jumps.
problem Improving numerical solutions for FBSDEs with jumps.
method Deep learning-based approach for decoupled FBSDEs with jumps.
result A priori and a posteriori error estimates for finite and infinite activity cases.
This paper presents an acceleration framework for packing linear programming problems where the amount of data available is limited, i.e., where the number of constraints m is small compared to the variable dimension n. The framework can be used as a black box to speed up linear programming solvers dramatically, by two…
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.
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.
DALTON improves ODE parameter estimation by learning from noisy data.
problem High sensitivity to parameters in ODEs produces unreliable parameter estimates.
method Data-adaptive probabilistic likelihood approximation for ODEs.
result DALTON produces more accurate parameter estimates than existing methods.
Quantum machine learning solves high-dimensional PDEs with lower variance and improved accuracy.
problem Approximating solutions to high-dimensional parabolic PDEs.
method Pure Variational Quantum Circuit (VQC) for BSDE approximation, using temporal discretization and Monte Carlo simulation.
result VQC achieves lower variance and improved accuracy in most cases, particularly in highly nonlinear regimes.
We formulate probabilistic numerical approximations to solutions of ordinary differential equations (ODEs) as problems in Gaussian process (GP) regression with non-linear measurement functions. This is achieved by defining the measurement sequence to consist of the observations of the difference between the derivative …
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 introduces a new method to solve complex PDEs efficiently.
problem Solving high-dimensional semilinear PDEs and BSDEs.
method Decomposes PDEs into linear and nonlinear parts, uses Deep BSDE solver with control variate method.
result Errors of the new method are much smaller than those of the original Deep BSDE solver.
Likelihood-free (a.k.a. simulation-based) inference problems are inverse problems with expensive, or intractable, forward models. ODE inverse problems are commonly treated as likelihood-free, as their forward map has to be numerically approximated by an ODE solver. This, however, is not a fundamental constraint but jus…
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.
New neural network approach solves Poisson equations efficiently.
problem Approximating solutions to Poisson equations with Dirichlet boundary conditions.
method Using shallow ReLUα-networks to solve Laplace operator equations. result Neural networks can approximate solutions to the Laplace operator with Dirichlet boundary conditions efficiently.
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.
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.
DC3 uses deep learning to solve hard-constrained optimization problems efficiently.
problem Hard constraints in optimization problems make classical solvers slow and infeasible.
method DC3 employs a differentiable procedure to enforce feasibility and unrolls corrections for inequality constraints.
result DC3 achieves near-optimal solutions while maintaining feasibility in both synthetic and real-world tasks.
New method reduces PDE surrogate model training costs by selectively acquiring time steps.
problem High computational cost of generating training data for PDE surrogate models.
method STAP (Selective Time-Step Acquisition for PDEs) framework that acquires only important time steps.
result Demonstrated effectiveness on several benchmark PDEs, reducing training costs.
This paper proposes a novel uncertainty quantification framework for computationally demanding systems characterized by a large vector of non-Gaussian uncertainties. It combines state-of-the-art techniques in advanced Monte Carlo sampling with Bayesian formulations. The key departure from existing works is the use of i…
Extends deep solver to FBSDEs with jumps for option pricing.
problem Solving FBSDEs with jumps for financial applications.
method Discretization, ANN parametrization, reinforcement learning, loss function minimization.
result Successfully applied to option pricing in low and high dimensions.
A new approach RA improves stochastic optimization by executing multiple steps between subsample updates.
problem Improving the efficiency and effectiveness of stochastic optimization methods.
method Developed Retrospective Approximation (RA) which executes multiple steps between subsample updates using a deterministic solver.
result RA achieves almost sure and L1 consistency under weak conditions and optimizes iteration and oracle complexity. Integrating logical reasoning within deep learning architectures has been a major goal of modern AI systems. In this paper, we propose a new direction toward this goal by introducing a differentiable (smoothed) maximum satisfiability (MAXSAT) solver that can be integrated into the loop of larger deep learning systems. …
There is resurging interest, in statistics and machine learning, in solvers for ordinary differential equations (ODEs) that return probability measures instead of point estimates. Recently, Conrad et al. introduced a sampling-based class of methods that are 'well-calibrated' in a specific sense. But the computational c…
A new method improves convergence in low-rank approximation.
problem Efficiently solving large-scale numerical linear algebra problems.
method Error-Powered Sketched Inverse Iteration (EPSI) Method.
result Convergence rate improves at least linearly with sketch size.
New method solves PDEs for any initial condition without retraining.
problem Solving PDEs for different initial conditions requires retraining neural solvers.
method Formulate solution as conditional probability distribution.
result Approximates PDE solution for arbitrary initial conditions.
Several algorithms for solving constraint satisfaction problems are based on survey propagation, a variational inference scheme used to obtain approximate marginal probability estimates for variable assignments. These marginals correspond to how frequently each variable is set to true among satisfying assignments, and …
This paper proposes a data-driven approach, by means of an Artificial Neural Network (ANN), to value financial options and to calculate implied volatilities with the aim of accelerating the corresponding numerical methods. With ANNs being universal function approximators, this method trains an optimized ANN on a data s…
We consider the problem of configuring general-purpose solvers to run efficiently on problem instances drawn from an unknown distribution. The goal of the configurator is to find a configuration that runs fast on average on most instances, and do so with the least amount of total work. It can run a chosen solver on a r…
Paper accelerates diffusion models, improving sampling speed.
problem Low sampling speed in score-based diffusion models.
method Design of novel training-free algorithms for deterministic and stochastic samplers.
result Accelerated samplers converge faster with improved rates.
Develops a new solver for path-dependent PDEs using signature kernels.
problem Solving path-dependent PDEs (PPDEs) efficiently and accurately.
method Uses signature kernels to solve PPDEs by approximating the solution with minimal norm in a reproducing kernel Hilbert space.
result Proves the consistency of the numerical scheme, ensuring convergence to PPDE solutions as the number of collocation points increases.
Physarum-inspired solver speeds up LP solving in neural networks.
problem Efficiently solving linear programming problems within neural networks.
method Inspired by Physarum dynamics, a differentiable solver for LPs.
result Solver outperforms existing methods in video segmentation and few-shot learning.
New method approximates POMDPs with PB-MDPs, providing error bounds and practical algorithms.
problem Difficulty in solving POMDPs with continuous or hybrid state and observation spaces.
method Bounding particle filtering error and adapting MDP algorithms to POMDPs.
result General theory and practical algorithms for POMDPs with no direct dependence on state and observation space sizes.
The paper tackles efficient computation of optimal transport by approximating conjugates with amortized optimization.
problem Efficient computation of convex conjugates in optimal transport is challenging and limits the quality of transport maps.
method The approach combines amortized approximations of conjugates with a fine-tuning solver to improve transport map quality.
result The method significantly improves the quality of transport maps for the Wasserstein-2 benchmark and models many 2D couplings and flows.
Understanding the global optimality in deep learning (DL) has been attracting more and more attention recently. Conventional DL solvers, however, have not been developed intentionally to seek for such global optimality. In this paper we propose a novel approximation algorithm, BPGrad, towards optimizing deep models glo…
New method uses Gaussian processes to improve PDE solver accuracy.
problem Uncertainty in PDE solver parameters and measurements.
method Physics-informed Gaussian process regression.
result Strictly generalizes weighted residual methods.
Develops a new solver for optimizing with stochastic dominance constraints.
problem Optimizing with stochastic dominance constraints is computationally expensive and impractical.
method Introduces Light Stochastic Dominance Solver (light-SD) that uses Lagrangian properties and surrogate approximation.
result The light-SD solver demonstrates superior performance on various problems.
New method combines ODE solvers with Bayesian inference for efficient model training.
problem Combining ODE solvers with Bayesian inference for efficient model training.
method Probabilistic state space model using extended Kalman filter for joint inference from differential equations and data.
result Efficient approximate Bayesian inference on latent force and ODE solution.
We propose a fast second-order method that can be used as a drop-in replacement for current deep learning solvers. Compared to stochastic gradient descent (SGD), it only requires two additional forward-mode automatic differentiation operations per iteration, which has a computational cost comparable to two standard for…
Efficiently solves MRF inference problems with semidefinite programming.
problem Computing partition function or MAP estimate in binary and multi-class MRFs.
method Coordinate-descent-based fast semidefinite solver for SDPs.
result Substantially outperforms existing state-of-the-art methods in approximate inference.
Probabilistic method combines space and time uncertainties in PDEs.
problem Separate treatment of space and time in PDE solvers obscures interactions and error quantification.
method Gaussian process interpretation of finite difference methods interacting with probabilistic ODE solvers.
result Joint quantification of space- and time-uncertainty possible without sacrificing ODE solver performance.
Diffusion models tackle noisy inverse problems with posterior sampling.
problem Efficiently solving general noisy inverse problems.
method Approximation of posterior sampling for diffusion models.
result Diffusion models can handle various noise statistics and nonlinear problems.
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.
Neural solver computes Wasserstein geodesics and velocity fields efficiently.
problem Computing Wasserstein geodesics and velocity fields efficiently.
method Sample-based neural network approach to solve the minimax problem.
result Directly samples from target distribution and estimates velocity field.
Paper accelerates diffusion models without retraining, reducing evaluations.
problem Approximating target data distributions efficiently.
method Training-free sampling algorithm using high-order Lagrange interpolation.
result Requires fewer score function evaluations than previous methods.
Neural Networks improve incompressible flow simulations without complex kernels.
problem Simulating incompressible flows accurately and efficiently.
method Integrates Neural Networks with Random Vortex Dynamics for incompressible Navier-Stokes equations.
result Strictly enforces physical properties like incompressibility and boundary conditions.
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.
We outline a new approach for solving optimization problems which enforce triangle inequalities on output variables. We refer to this as metric-constrained optimization, and give several examples where problems of this form arise in machine learning applications and theoretical approximation algorithms for graph cluste…
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.
Continuous-time optimal stopping solved with deep reinforcement learning
problem Optimal stopping problems in continuous time
method CARLOS (Continuous-time Adaptive Reinforcement Learning for Optimal Stopping)
result Higher prices than existing Bermudan solvers, approaching American upper bound
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.