Transport away your problems: Calibrating stochastic simulations with optimal transport

• URL: http://arxiv.org/abs/2107.08648v1
• Date: Mon, 19 Jul 2021 07:11:13 GMT
• Title: Transport away your problems: Calibrating stochastic simulations with optimal transport
• Authors: Chris Pollard, Philipp Windischhofer
• Abstract summary: We leverage methods from transportation theory to construct "calibrated" simulators. We use a neural network to compute minimal modifications to the individual samples produced by the simulator. We illustrate the method and its benefits in the context of experimental particle physics.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Stochastic simulators are an indispensable tool in many branches of science. Often based on first principles, they deliver a series of samples whose distribution implicitly defines a probability measure to describe the phenomena of interest. However, the fidelity of these simulators is not always sufficient for all scientific purposes, necessitating the construction of ad-hoc corrections to "calibrate" the simulation and ensure that its output is a faithful representation of reality. In this paper, we leverage methods from transportation theory to construct such corrections in a systematic way. We use a neural network to compute minimal modifications to the individual samples produced by the simulator such that the resulting distribution becomes properly calibrated. We illustrate the method and its benefits in the context of experimental particle physics, where the need for calibrated stochastic simulators is particularly pronounced.

Related papers

• Bayesian Adaptive Calibration and Optimal Design [16.821341360894706]
  Current machine learning approaches mostly rely on rerunning simulations over a fixed set of designs available in the observed data. We propose a data-efficient algorithm to run maximally informative simulations within a batch-sequential process. We show the benefits of our method when compared to related approaches across synthetic and real-data problems.
  arXiv  Detail & Related papers  (2024-05-23T11:14:35Z)
• SIP: Injecting a Structural Inductive Bias into a Seq2Seq Model by Simulation [75.14793516745374]
  We show how a structural inductive bias can be efficiently injected into a seq2seq model by pre-training it to simulate structural transformations on synthetic data. Our experiments show that our method imparts the desired inductive bias, resulting in better few-shot learning for FST-like tasks.
  arXiv  Detail & Related papers  (2023-10-01T21:19:12Z)
• Importance sampling for stochastic quantum simulations [68.8204255655161]
  We introduce the qDrift protocol, which builds random product formulas by sampling from the Hamiltonian according to the coefficients. We show that the simulation cost can be reduced while achieving the same accuracy, by considering the individual simulation cost during the sampling stage. Results are confirmed by numerical simulations performed on a lattice nuclear effective field theory.
  arXiv  Detail & Related papers  (2022-12-12T15:06:32Z)
• Fast emulation of density functional theory simulations using approximate Gaussian processes [0.6445605125467573]
  A second statistical model that predicts the simulation output can be used in lieu of the full simulation during model fitting. We use the emulators to calibrate, in a Bayesian manner, the density functional theory (DFT) model parameters using observed data. The utility of these DFT models is to make predictions, based on observed data, about the properties of experimentally unobserved nuclides.
  arXiv  Detail & Related papers  (2022-08-24T05:09:36Z)
• Physics-informed machine learning with differentiable programming for heterogeneous underground reservoir pressure management [64.17887333976593]
  Avoiding over-pressurization in subsurface reservoirs is critical for applications like CO2 sequestration and wastewater injection. Managing the pressures by controlling injection/extraction are challenging because of complex heterogeneity in the subsurface. We use differentiable programming with a full-physics model and machine learning to determine the fluid extraction rates that prevent over-pressurization.
  arXiv  Detail & Related papers  (2022-06-21T20:38:13Z)
• Fast and realistic large-scale structure from machine-learning-augmented random field simulations [0.0]
  We train a machine learning model to transform projected lognormal dark matter density fields to more realistic dark matter maps. We demonstrate the performance of our model comparing various statistical tests with different field resolutions, redshifts and cosmological parameters.
  arXiv  Detail & Related papers  (2022-05-16T18:00:01Z)
• Likelihood-Free Inference in State-Space Models with Unknown Dynamics [71.94716503075645]
  We introduce a method for inferring and predicting latent states in state-space models where observations can only be simulated, and transition dynamics are unknown. We propose a way of doing likelihood-free inference (LFI) of states and state prediction with a limited number of simulations.
  arXiv  Detail & Related papers  (2021-11-02T12:33:42Z)
• Unrolling Particles: Unsupervised Learning of Sampling Distributions [102.72972137287728]
  Particle filtering is used to compute good nonlinear estimates of complex systems. We show in simulations that the resulting particle filter yields good estimates in a wide range of scenarios.
  arXiv  Detail & Related papers  (2021-10-06T16:58:34Z)
• Transfer learning suppresses simulation bias in predictive models built from sparse, multi-modal data [15.587831925516957]
  Many problems in science, engineering, and business require making predictions based on very few observations. To build a robust predictive model, these sparse data may need to be augmented with simulated data, especially when the design space is multidimensional. We combine recent developments in deep learning to build more robust predictive models from multimodal data.
  arXiv  Detail & Related papers  (2021-04-19T23:28:32Z)
• A Doubly Stochastic Simulator with Applications in Arrivals Modeling and Simulation [8.808993671472349]
  We propose a framework that integrates classical Monte Carlo simulators and Wasserstein generative adversarial networks to model, estimate, and simulate a broad class of arrival processes. Classical Monte Carlo simulators have advantages at capturing interpretable "physics" of a Poisson object, whereas neural-network-based simulators have advantages at capturing less-interpretable complicated dependence within a high-dimensional distribution.
  arXiv  Detail & Related papers  (2020-12-27T13:32:16Z)
• Learning to predict metal deformations in hot-rolling processes [59.00006390882099]
  Hot-rolling is a metal forming process that produces a cross-section from an input through a sequence of deformations. In current practice, the rolling sequence and the geometry of their rolls are needed to achieve a given cross-section. We propose a supervised learning approach to predict a given by a set of rolls with given geometry.
  arXiv  Detail & Related papers  (2020-07-22T13:33:44Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.