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.
Efficient numerical method for time-fractional Black-Scholes model.
problem Solving time-fractional Black-Scholes equations for European options.
method Crank-Nicolson discretization for time, exponential B-spline for space.
result The proposed method is unconditionally stable and superior to existing approaches.
Investigates stability of piecewise flat Ricci flow using analysis and simulations.
problem Stability of piecewise flat Ricci flow.
method Linear stability analysis and numerical simulations.
result Adaptations avoided numerical instability and led to convergence to smooth solutions.
Develops methods to simulate option prices for a specific stochastic volatility model.
problem No method exists to compute option prices numerically for a non-martingale jump-type model.
method Develops two Monte Carlo simulation methods under change of measure.
result Conducts numerical experiments to validate the developed methods.
By using numerical simulation, we confirm that Takayasu--Sato--Takayasu (TST) model which leads Pareto's law satisfies the detailed balance under Gibrat's law. In the simulation, we take an exponential tent-shaped function as the growth rate distribution. We also numerically confirm the reflection law equivalent to the…
Numerical simulations show stability of Type-II singularities in noncompact hypersurfaces.
problem Stability of Type-II singularities in noncompact hypersurfaces with rotationally-symmetric perturbations.
method Adaptation of the overlap method to include angular dependence.
result MCF of noncompact hypersurfaces with angular dependence behaves similarly to rotationally-symmetric perturbations, developing Type-II or Type-I singularities.
A neural network approach to compute stable metrics for numerical simulation data.
problem Computing stable and generalizing metrics for diverse numerical simulation data.
method A Siamese neural network architecture with a specialized loss function trained on a controlled data generation setup.
result LSiM outperforms existing metrics for vector spaces and image-based metrics.
Paper simulates LR fuzzy intervals with interval-valued cores.
problem Generating random fuzzy intervals with interval-valued cores.
method Developed algorithms for simulating LR fuzzy numbers with interval-valued cores.
result Numerically efficient algorithm for simulating fuzzy values.
A new method simulates square-root processes efficiently.
problem Simulating square-root processes accurately and efficiently.
method Simulate the integrated square-root process instead of the square-root process itself.
result High precision with low number of time steps, and exact limiting Inverse Gaussian distributions.
GPU speeds up Monte Carlo simulations for large time steps.
problem Slow convergence and inaccurate solutions with large time steps in Monte Carlo simulations.
method Generalizes the Seven League scheme for GPU acceleration.
result Significantly improved computational speed.
In this manuscript we introduce numerical Gaussian process Kalman filtering (GPKF). Numerical Gaussian processes have recently been developed to simulate spatiotemporal models. The contribution of this paper is to embed numerical Gaussian processes into the recursive Kalman filter equations. This embedding enables us t…
Improved ANN-based Monte Carlo simulation for Higgs decay events.
problem Accurate simulation of Higgs boson decay events.
method Monte Carlo simulation using an Artificial Neural Network (ANN) with improved training algorithm.
result The ANN simulation of Higgs decay is within 0.7% of the true value and achieves 26% unweighting efficiency.
Improved nested simulation for financial risk measurement.
problem Efficiently estimating nested risk measures in financial engineering.
method Reusing inner simulation outputs to improve efficiency and accuracy.
result The proposed approach outperforms standard nested simulation and regression methods.
We introduce a new deep-learning based algorithm to evaluate options in affine rough stochastic volatility models. Viewing the pricing function as the solution to a curve-dependent PDE (CPDE), depending on forward curves rather than the whole path of the process, for which we develop a numerical scheme based on deep le…
New simulation technique speeds up Lévy-driven OU process pricing.
problem Inefficient Monte Carlo simulations of Lévy-driven OU processes.
method Numerical inversion of characteristic function combined with FFT for fast and accurate simulations.
result The proposed technique is at least one order of magnitude faster than existing methods.
Study simulates Variance Gamma processes for energy derivatives pricing.
problem Simulating Variance Gamma processes for accurate energy derivative pricing.
method Three-step procedure to relate self-decomposability to increments, derived from Qu et al. (2019). Exact simulation of skeleton of Variance Gamma and symmetric Variance Gamma driven Ornstein-Uhlenbeck processes.
result Exact simulation of Variance Gamma and related processes without numerical inversion.
Method improves simulation accuracy by mitigating distribution shift in hybrid systems.
problem Mitigating distribution shift in machine-learning augmented hybrid simulation.
method Tangent-space regularized estimator to control distribution shift.
result Marked improvements in simulation accuracy, especially for systems with high distribution shift.
ISALT uses inference to simulate SDEs with large time-steps, improving efficiency.
problem Efficiently simulating ergodic SDEs with large time-steps.
method Inference-based schemes adaptive to large time-steps (ISALT) from data.
result ISALT achieves significant time reduction and optimal accuracy.
Accurate forward modeling is important for solving inverse problems. An inaccurate wave-equation simulation, as a forward operator, will offset the results obtained via inversion. In this work, we consider the case where we deal with incomplete physics. One proxy of incomplete physics is an inaccurate discretization of…
Geometric integrator preserves coadjoint orbits in dissipative systems.
problem Preserving coadjoint orbits in dissipative mechanical systems.
method Adapted discrete variational integrators for forced Euler-Poincaré and Lie-Poisson systems.
result Preserves coadjoint orbits exactly, improving over general-purpose methods.
In this paper, we investigate a numerical algorithm for the pricing of swing options, relying on the so-called optimal quantization method. The numerical procedure is described in details and numerous simulations are provided to assert its efficiency. In particular, we carry out a comparison with the Longstaff-Schwartz…
Two methods improve simulation of European call options under Heston model.
problem Efficient simulation of European call options under Heston model.
method Two strongly convergent and positivity-preserving methods for Cox-Ingersoll-Ross process under Lamperti transformation: truncated Euler and backward Euler methods.
result Explicit truncated Euler method is computationally effective and robust under high volatility, while implicit backward Euler method provides high accuracy and stability.
NeuralMD accelerates protein-ligand binding simulations 1Kx faster.
problem Accurate and efficient simulation of protein-ligand binding dynamics.
method Physics-informed multi-grained group symmetric framework with BindingNet and augmented neural differential equation solver.
result Achieves over 1Kx speedup and up to 15x reduction in reconstruction error compared to standard methods.
Develops efficient methods for approximating densities of financial models with jumps.
problem Approximating densities of affine jump diffusions with state-independent jump intensities.
method Recursive approach for deriving closed-form solutions to moments, constructing density approximations via moment matching.
result Superior computational efficiency and precision in option pricing and simulation compared to existing techniques.
New method transforms complex stochastic equations into simpler ones for efficient simulation.
problem Efficient simulation of complex path-dependent stochastic processes.
method Transforms Volterra-type SDEs into standard diffusion processes using convolution kernels.
result Proposes a numerical simulation scheme with a strong convergence rate of 1/2.
Develops numerical methods for pricing exchange options in a market with limited liquidity.
problem Pricing European style exchange options in a market with finite liquidity.
method Integrates price impact into the dynamics of correlated assets using a controlled variate approach.
result Numerical pricing methods for exchange options are developed and validated.
Medical imaging systems are commonly assessed by use of objective image quality measures. Supervised deep learning methods have been investigated to implement numerical observers for task-based image quality assessment. However, labeling large amounts of experimental data to train deep neural networks is tedious, expen…
The goal of this paper is to assess the utility of Reduced-Order Models (ROMs) developed from 3D physics-based models for predicting transient thermal power output for an enhanced geothermal reservoir while explicitly accounting for uncertainties in the subsurface system and site-specific details. Numerical simulations…
Optical scatterometry is a method to measure the size and shape of periodic micro- or nanostructures on surfaces. For this purpose the geometry parameters of the structures are obtained by reproducing experimental measurement results through numerical simulations. We compare the performance of Bayesian optimization to …
Deep neural networks provide meaningful uncertainty estimates for large-scale simulations.
problem Uncertainty estimates for deep neural network predictions from large-scale simulations.
method General variational inference approach to calibrate Bayesian uncertainties.
result Calibrated Bayesian uncertainties preserved physics-correlations in predicted quantities.
Continuous time stochastic processes are useful models especially for financial and insurance purposes. The numerical simulation of such models is dependant of the time discrete discretization, of the parametric estimation and of the choice of a random number generator. The aim of this paper is to provide the tools for…
Deep learning accelerates Monte Carlo SDE simulations with large time steps.
problem Accurate simulation of SDEs with large time steps.
method Polynomial chaos expansion with neural network learned stochastic collocation points.
result Data-driven scheme achieves strong convergence in Monte Carlo simulations.
ξ-torch simplifies physics-informed learning by providing differentiable functionals.
problem Training physics-informed deep neural networks requires differentiable physical simulations.
method ξ-torch offers a library of differentiable functionals for scientific simulations.
result Improves numerical stability and reduces memory requirements for higher order derivatives.
Modeling counterparty risk is computationally challenging because it requires the simultaneous evaluation of all the trades with each counterparty under both market and credit risk. We present a multi-Gaussian process regression approach, which is well suited for OTC derivative portfolio valuation involved in CVA compu…
The objective for this work is to develop a data-driven proxy to high-fidelity numerical flow simulations using digital images. The proposed model can capture the flow field and permeability in a large verity of digital porous media based on solid grain geometry and pore size distribution by detailed analyses of the lo…
Simulates risk-neutral markets using neural spline flows.
problem Creating realistic risk-neutral market simulations.
method Developed a low-dimensional martingale representation and used neural spline flows for sampling.
result The calibrated simulator is closest to historical data with respect to Kullback-Leibler divergence.
In this article, we propose an exact simulation method of the Wishart multidimensional stochastic volatility (WMSV) model, which was recently introduced by Da Fonseca et al. \cite{DGT08}. Our method is based onanalysis of the conditional characteristic function of the log-price given volatility level. In particular, we…
Efficient simulation scheme for rough Heston model reduces computational cost.
problem Accurate and efficient simulation of the rough Heston model for option pricing.
method Weak simulation scheme based on Markovian approximations of the rough Heston process.
result The new scheme exhibits second order weak convergence with linear computational cost.
We study polygonal analogues of several moving boundary problems and their time discretization which preserves the constant area speed property. We establish various polygonal analogues of geometric formulas for moving boundaries and make use of the geometric formulas for our numerical scheme and its analysis of genera…
A new fast method simulates stochastic volatility models.
problem Simulating stochastic volatility models efficiently.
method Karhunen-Loève expansions to express stochastic volatility as sine series, followed by analytical derivation of integrals.
result Simulation is several hundred times faster than existing methods.
We first estimate the average growth of a company's annual income and its variance by using both real company data and a numerical model which we already introduced a couple of years ago. Investment strategies expecting for income growth is evaluated based on the numerical model. Our numerical simulation suggests the p…
Developed a simulation method for 3/2 stochastic volatility model.
problem Pricing options in the 3/2 stochastic volatility model.
method Explicit weak solution for the 3/2 model, using inverse CIR process property.
result Simulation algorithm performance comparable to other methods.
Recent years have seen an increased level of interest in pricing equity options under a stochastic volatility model such as the Heston model. Often, simulating a Heston model is difficult, as a standard finite difference scheme may lead to significant bias in the simulation result. Reducing the bias to an acceptable le…
E&E uses contrastive learning to speed up SBI for high-dimensional systems.
problem Challenges in training high-dimensional emulators for complex systems.
method Contrastive learning for low-dimensional latent embedding and fast emulator.
result Superior performance in non-identifiable parameter estimation tasks.
Optimizes control of infectious disease spread using stochastic methods.
problem Optimizing control of highly infectious diseases like COVID-19.
method Reformulated Hamilton-Jacobi-Bellman equation as stochastic minimum principle, leading to forward-backward stochastic differential equations.
result Numerous numerical solutions presented under various scenarios.
Machine learning models predict the behavior of negatively buoyant jets from wastewater.
problem Minimizing harmful effects of negatively buoyant jets during wastewater discharge.
method Training machine learning models (ANN, XGBoost, CatBoost, LightGBM) on OpenFOAM simulations and experimental data.
result Artificial Neural Network provided the best prediction with R2 0.98 and RMSE 0.28.
Neural network factorization speeds up Vlasov equation simulations.
problem Accelerating simulations of collisionless plasma described by the Vlasov equation.
method Data-driven low-rank matrix factorization using convolutional neural networks.
result The method outperforms standard linear algebra at inference time.
Extracts coarse-grained PDEs from microscopic simulations.
problem Discovering effective PDEs for macro-scale processes from microscopic data.
method Combining neural networks with equation-free numerics and data-driven approaches.
result Efficiently discovers macro-scale PDEs from microscopic simulations.