ODE - square of differential equation
$begingroup$
I have an initial-value ODE of the type
$qquad qquad qquad frac{dx}{dt} = f(x), quad x(t_0) = x_0 in R^n$
where $f$ is Lipschitz but not differentiable.
Since n is quite big in my problem, I need to use an efficient solver which is also prone to parallel processing.
I have recently seen a perfect ODE solution published in NIPS, called neural ODE, which is a part of pytorch and is inherently possible to use GPU. However, I realized that it is required that f to be differentiable.
I played with $f$ a bit, and I found out that $f(x)^T f(x)$ is differentiable. Thus, I was thinking about somehow the solving the following ODE
$qquad qquad qquad big(frac{dx}{dt}big)^2 = f(x)^T f(x)$.
Is there anybody who be aware of such techniques?
Any help is highly appreciated.
ordinary-differential-equations
edited Dec 28 '18 at 10:53
Ahmad Bazzi
8,5212824
asked Dec 28 '18 at 10:20
Majid MohammadiMajid Mohammadi
275
$endgroup$
add a comment |
$begingroup$
I have an initial-value ODE of the type
$qquad qquad qquad frac{dx}{dt} = f(x), quad x(t_0) = x_0 in R^n$
where $f$ is Lipschitz but not differentiable.
Since n is quite big in my problem, I need to use an efficient solver which is also prone to parallel processing.
I have recently seen a perfect ODE solution published in NIPS, called neural ODE, which is a part of pytorch and is inherently possible to use GPU. However, I realized that it is required that f to be differentiable.
I played with $f$ a bit, and I found out that $f(x)^T f(x)$ is differentiable. Thus, I was thinking about somehow the solving the following ODE
$qquad qquad qquad big(frac{dx}{dt}big)^2 = f(x)^T f(x)$.
Is there anybody who be aware of such techniques?
Any help is highly appreciated.
ordinary-differential-equations
edited Dec 28 '18 at 10:53
Ahmad Bazzi
8,5212824
asked Dec 28 '18 at 10:20
Majid MohammadiMajid Mohammadi
275
$endgroup$
add a comment |
$begingroup$
I have an initial-value ODE of the type
$qquad qquad qquad frac{dx}{dt} = f(x), quad x(t_0) = x_0 in R^n$
where $f$ is Lipschitz but not differentiable.
Since n is quite big in my problem, I need to use an efficient solver which is also prone to parallel processing.
I have recently seen a perfect ODE solution published in NIPS, called neural ODE, which is a part of pytorch and is inherently possible to use GPU. However, I realized that it is required that f to be differentiable.
I played with $f$ a bit, and I found out that $f(x)^T f(x)$ is differentiable. Thus, I was thinking about somehow the solving the following ODE
$qquad qquad qquad big(frac{dx}{dt}big)^2 = f(x)^T f(x)$.
Is there anybody who be aware of such techniques?
Any help is highly appreciated.
ordinary-differential-equations
edited Dec 28 '18 at 10:53
Ahmad Bazzi
8,5212824
asked Dec 28 '18 at 10:20
Majid MohammadiMajid Mohammadi
275
$endgroup$
I have an initial-value ODE of the type
$qquad qquad qquad frac{dx}{dt} = f(x), quad x(t_0) = x_0 in R^n$
where $f$ is Lipschitz but not differentiable.
Since n is quite big in my problem, I need to use an efficient solver which is also prone to parallel processing.
I have recently seen a perfect ODE solution published in NIPS, called neural ODE, which is a part of pytorch and is inherently possible to use GPU. However, I realized that it is required that f to be differentiable.
I played with $f$ a bit, and I found out that $f(x)^T f(x)$ is differentiable. Thus, I was thinking about somehow the solving the following ODE
$qquad qquad qquad big(frac{dx}{dt}big)^2 = f(x)^T f(x)$.
Is there anybody who be aware of such techniques?
Any help is highly appreciated.
ordinary-differential-equations
ordinary-differential-equations
edited Dec 28 '18 at 10:53
Ahmad Bazzi
8,5212824
asked Dec 28 '18 at 10:20
Majid MohammadiMajid Mohammadi
275
edited Dec 28 '18 at 10:53
Ahmad Bazzi
8,5212824
asked Dec 28 '18 at 10:20
Majid MohammadiMajid Mohammadi
275
edited Dec 28 '18 at 10:53
Ahmad Bazzi
8,5212824
edited Dec 28 '18 at 10:53
Ahmad Bazzi
8,5212824
edited Dec 28 '18 at 10:53
Ahmad Bazzi
8,5212824
8,5212824
asked Dec 28 '18 at 10:20
Majid MohammadiMajid Mohammadi
275
asked Dec 28 '18 at 10:20
Majid MohammadiMajid Mohammadi
275
asked Dec 28 '18 at 10:20
Majid MohammadiMajid Mohammadi
275
275
add a comment |
add a comment |
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