129 research outputs found
The Jormungand Climate Model
The geological and paleomagnetic record indicate that around 750 million and 580 millions years ago glaciers grew near the equator, though as of yet we do not fully understand the nature of these glaciations. The well-known Snowball Earth Hypothesis states that the Earth was covered entirely by glaciers. However, it is hard for this hypothesis to account for certain aspects of the biological evidence such as the survival of photosynthetic eukaryotes. Thus the Jormungand Hypothesis was developed as an alternative to the Snowball Earth Hypothesis. In this paper we investigate previous models of the Jormungand state and look at the dynamics of the Hadley cells to develop a new model to represent the Jormungand Hypothesis. We end by solving for an analytical approximation to the model using a finite Legendre expansion and geometric singular perturbation theory. The resultant model gives a stable equilibrium point near the equator with strong hysteresis that satisfies the Jormungand Hypothesis
The Jormungand Climate Model
The geological and paleomagnetic record indicate that around 750 million and 580 millions years ago glaciers grew near the equator, though as of yet we do not fully understand the nature of these glaciations. The well-known Snowball Earth Hypothesis states that the Earth was covered entirely by glaciers. However, it is hard for this hypothesis to account for certain aspects of the biological evidence such as the survival of photosynthetic eukaryotes. Thus the Jormungand Hypothesis was developed as an alternative to the Snowball Earth Hypothesis. In this paper we investigate previous models of the Jormungand state and look at the dynamics of the Hadley cells to develop a new model to represent the Jormungand Hypothesis. We end by solving for an analytical approximation to the model using a finite Legendre expansion and geometric singular perturbation theory. The resultant model gives a stable equilibrium point near the equator with strong hysteresis that satisfies the Jormungand Hypothesis
The Jormungand Climate Model
The geological and paleomagnetic record indicate that around 750 million and 580 millions years ago glaciers grew near the equator, though as of yet we do not fully understand the nature of these glaciations. The well-known Snowball Earth Hypothesis states that the Earth was covered entirely by glaciers. However, it is hard for this hypothesis to account for certain aspects of the biological evidence such as the survival of photosynthetic eukaryotes. Thus the Jormungand Hypothesis was developed as an alternative to the Snowball Earth Hypothesis. In this paper we investigate previous models of the Jormungand state and look at the dynamics of the Hadley cells to develop a new model to represent the Jormungand Hypothesis. We end by solving for an analytical approximation to the model using a finite Legendre expansion and geometric singular perturbation theory. The resultant model gives a stable equilibrium point near the equator with strong hysteresis that satisfies the Jormungand Hypothesis
The Jormungand Climate Model
The geological and paleomagnetic record indicate that around 750 million and 580 millions years ago glaciers grew near the equator, though as of yet we do not fully understand the nature of these glaciations. The well-known Snowball Earth Hypothesis states that the Earth was covered entirely by glaciers. However, it is hard for this hypothesis to account for certain aspects of the biological evidence such as the survival of photosynthetic eukaryotes. Thus the Jormungand Hypothesis was developed as an alternative to the Snowball Earth Hypothesis. In this paper we investigate previous models of the Jormungand state and look at the dynamics of the Hadley cells to develop a new model to represent the Jormungand Hypothesis. We end by solving for an analytical approximation to the model using a finite Legendre expansion and geometric singular perturbation theory. The resultant model gives a stable equilibrium point near the equator with strong hysteresis that satisfies the Jormungand Hypothesis
Confederated Modular Differential Equation APIs for Accelerated Algorithm Development and Benchmarking
Performant numerical solving of differential equations is required for
large-scale scientific modeling. In this manuscript we focus on two questions:
(1) how can researchers empirically verify theoretical advances and
consistently compare methods in production software settings and (2) how can
users (scientific domain experts) keep up with the state-of-the-art methods to
select those which are most appropriate? Here we describe how the confederated
modular API of DifferentialEquations.jl addresses these concerns. We detail the
package-free API which allows numerical methods researchers to readily utilize
and benchmark any compatible method directly in full-scale scientific
applications. In addition, we describe how the complexity of the method choices
is abstracted via a polyalgorithm. We show how scientific tooling built on top
of DifferentialEquations.jl, such as packages for dynamical systems
quantification and quantum optics simulation, both benefit from this structure
and provide themselves as convenient benchmarking tools.Comment: 4 figures, 3 algorithm
A machine learning aided global diagnostic and comparative tool to assess effect of quarantine control in Covid-19 spread
We have developed a globally applicable diagnostic Covid-19 model by
augmenting the classical SIR epidemiological model with a neural network
module. Our model does not rely upon previous epidemics like SARS/MERS and all
parameters are optimized via machine learning algorithms employed on publicly
available Covid-19 data. The model decomposes the contributions to the
infection timeseries to analyze and compare the role of quarantine control
policies employed in highly affected regions of Europe, North America, South
America and Asia in controlling the spread of the virus. For all continents
considered, our results show a generally strong correlation between
strengthening of the quarantine controls as learnt by the model and actions
taken by the regions' respective governments. Finally, we have hosted our
quarantine diagnosis results for the top 70 affected countries worldwide, on a
public platform, which can be used for informed decision making by public
health officials and researchers alike.Comment: 21 pages, 16 figure
Locally Regularized Neural Differential Equations: Some Black Boxes Were Meant to Remain Closed!
Implicit layer deep learning techniques, like Neural Differential Equations,
have become an important modeling framework due to their ability to adapt to
new problems automatically. Training a neural differential equation is
effectively a search over a space of plausible dynamical systems. However,
controlling the computational cost for these models is difficult since it
relies on the number of steps the adaptive solver takes. Most prior works have
used higher-order methods to reduce prediction timings while greatly increasing
training time or reducing both training and prediction timings by relying on
specific training algorithms, which are harder to use as a drop-in replacement
due to strict requirements on automatic differentiation. In this manuscript, we
use internal cost heuristics of adaptive differential equation solvers at
stochastic time points to guide the training toward learning a dynamical system
that is easier to integrate. We "close the black-box" and allow the use of our
method with any adjoint technique for gradient calculations of the differential
equation solution. We perform experimental studies to compare our method to
global regularization to show that we attain similar performance numbers
without compromising the flexibility of implementation on ordinary differential
equations (ODEs) and stochastic differential equations (SDEs). We develop two
sampling strategies to trade off between performance and training time. Our
method reduces the number of function evaluations to 0.556-0.733x and
accelerates predictions by 1.3-2x
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