# LEARNING STOCHASTIC DIFFERENTIAL EQUATIONS WITH GAUSSIAN PROCESSES WITHOUT GRADIENT MATCHING

@article{Yildiz2018LEARNINGSD, title={LEARNING STOCHASTIC DIFFERENTIAL EQUATIONS WITH GAUSSIAN PROCESSES WITHOUT GRADIENT MATCHING}, author={Çagatay Yildiz and Markus Heinonen and Jukka Intosalmi and Henrik Mannerstr{\"o}m and Harri L{\"a}hdesm{\"a}ki}, journal={2018 IEEE 28th International Workshop on Machine Learning for Signal Processing (MLSP)}, year={2018}, pages={1-6} }

We introduce a novel paradigm for learning non-parametric drift and diffusion functions for stochastic differential equation (SDE). The proposed model learns to simulate path distributions that match observations with non-uniform time increments and arbitrary sparseness, which is in contrast with gradient matching that does not optimize simulated responses. We formulate sensitivity equations for learning and demonstrate that our general stochastic distribution optimisation leads to robust and…

## 21 Citations

Deep learning with differential Gaussian process flows

- Computer ScienceAISTATS
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A novel deep learning paradigm of differential flows that learn a stochastic differential equation transformations of inputs prior to a standard classification or regression function is proposed, demonstrating excellent results as compared to deep Gaussian processes and Bayesian neural networks.

Sparse Gaussian Processes for Stochastic Differential Equations

- Computer Science
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An approximate (variational) inference algorithm is derived and a novel parameterization of the approximate distribution over paths using a sparse Markovian Gaussian process is proposed, allowing the usage of well-established optimizing algorithms such as natural gradient descent for better convergence.

Learning stochastic dynamical systems with neural networks mimicking the Euler-Maruyama scheme

- Computer Science2021 29th European Signal Processing Conference (EUSIPCO)
- 2021

A data driven approach where parameters of the SDE are represented by a neural network with a built-in SDE integration scheme and the loss function is based on a maximum likelihood criterion, under order one Markov Gaussian assumptions.

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- 2021

This approach does not require long trajectories, works on scattered snapshot data, and is designed to naturally handle diﬀerent time steps per snapshot, which lends themselves naturally to “physics-informed” gray-box identiﬁcation when approximate coarse models, such as mean means equations, are available.

Infinite-dimensional optimization and Bayesian nonparametric learning of stochastic differential equations

- MathematicsArXiv
- 2022

The paper has two major themes. The first part of the paper establishes certain general results for infinite-dimensional optimization problems on Hilbert spaces. These results cover the classical…

Monotonic Gaussian Process Flows

- Computer ScienceAISTATS
- 2020

A nonparametric model of monotonic functions that allows for interpretable priors and principled quantification of hierarchical uncertainty is derived and it is demonstrated that the efficacy of the proposed model is demonstrated by providing competitive results to other probabilistic Monotonic models on a number of benchmark functions.

Learning effective stochastic differential equations from microscopic simulations: combining stochastic numerics and deep learning

- Computer ScienceArXiv
- 2021

This work identifies effective stochastic differential equations for coarse observables of fine-grained particleor agent-based simulations and approximate the drift and diffusivity functions in these effective SDE through neural networks, which can be thought of as effective stoChastic ResNets.

Monotonic Gaussian Process Flow

- Computer ScienceArXiv
- 2019

A nonparametric model of monotonic functions that allows for interpretable priors and principled quantification of hierarchical uncertainty is derived and it is demonstrated that the efficacy of the proposed model is demonstrated by providing competitive results to other probabilistic Monotonic models on a number of benchmark functions.

A Nonparametric Spatio-temporal SDE Model

- Mathematics, Computer ScienceNIPS 2018
- 2018

The experiments demonstrate that the spatio-temporal model is better able to fit a real world data set that has complex dynamics than the spatial model, and can also reduce the forecasting error.

A Nonparametric Spatio-temporal SDE Model

- Mathematics, Computer Science
- 2018

We propose a nonparametric spatio-temporal stochastic differential equation (SDE) 1 model that can learn the underlying dynamics of arbitrary continuous-time systems 2 without prior knowledge. We…

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