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Neural ordinary differential equations
We introduce a new family of deep neural network models. Instead of specifying a discrete
sequence of hidden layers, we parameterize the derivative of the hidden state using a …
sequence of hidden layers, we parameterize the derivative of the hidden state using a …
Scalable gradients for stochastic differential equations
The adjoint sensitivity method scalably computes gradients of solutions to ordinary
differential equations. We generalize this method to stochastic differential equations …
differential equations. We generalize this method to stochastic differential equations …
Neural jump stochastic differential equations
Many time series are effectively generated by a combination of deterministic continuous
flows along with discrete jumps sparked by stochastic events. However, we usually do not …
flows along with discrete jumps sparked by stochastic events. However, we usually do not …
Considering discrepancy when calibrating a mechanistic electrophysiology model
Uncertainty quantification (UQ) is a vital step in using mathematical models and simulations
to take decisions. The field of cardiac simulation has begun to explore and adopt UQ …
to take decisions. The field of cardiac simulation has begun to explore and adopt UQ …
Neural stochastic differential equations: Deep latent gaussian models in the diffusion limit
B Tzen, M Raginsky - ar** review of opportunities and challenges
Integrating prior epidemiological knowledge embedded within mechanistic models with the
data-mining capabilities of artificial intelligence (AI) offers transformative potential for …
data-mining capabilities of artificial intelligence (AI) offers transformative potential for …
Infinitely deep bayesian neural networks with stochastic differential equations
We perform scalable approximate inference in continuous-depth Bayesian neural networks.
In this model class, uncertainty about separate weights in each layer gives hidden units that …
In this model class, uncertainty about separate weights in each layer gives hidden units that …
Neural jump ordinary differential equations: Consistent continuous-time prediction and filtering
Combinations of neural ODEs with recurrent neural networks (RNN), like GRU-ODE-Bayes
or ODE-RNN are well suited to model irregularly observed time series. While those models …
or ODE-RNN are well suited to model irregularly observed time series. While those models …