20
votes
Accepted
Use of machine learning in computational fluid dynamics
It's a long-running joke that CFD stands for "colorful fluid dynamics". Nevertheless, it is used -- and useful -- in a wide range of applications.
I believe your discontent stems from not ...
- 12k
20
votes
Accepted
Sensitivity of $y$ w.r.t. to $x$ in $y=f(x)$ where f is a routine
The act of using automatic differentiation for derivative calculations of general programs has become known as differentiable programming. There are many grades of differentiable programming across ...
- 12k
17
votes
Accepted
Why aren't Krylov subspace methods popular in the Machine Learning community compared to Gradient Descent?
On a basic level, I don't buy the argument that you have to "solve a linear system for many machine learning algorithms". Much more, you usually have to optimize a non-linear equation which ...
- 2,862
12
votes
Faster Logistic Function
Yes! There are nice approximations of the logistic.
Plot of Approximating Functions
As shown below, several functions approximate the logistic (shown as blue dots). This graph is available ...
- 3,566
11
votes
Accepted
Markov (Chain) image generators?
I've implemented this recently, basically it counts how many times each specific colour borders another colour to make up a frequency table. To generate an image, a random colour and position are ...
- 226
11
votes
Are there tasks in machine learning which require double precision floating points?
I am not an expert in machine learning, but I can outline the considerations that are relevant.
The numerical calculations in machine learning are generally linear algebra -- either solving linear ...
- 16.3k
7
votes
Use of machine learning in computational fluid dynamics
I think you are mixing a couple different ideas that are causing confusion. Yes, there are a wide variety of ways to discretize a given problem. Choosing an appropriate way may look like "voodoo" ...
- 4,577
7
votes
Seeking a free symbolic regression software
I wrote a Python package called PyPGE.
PyPGE is a Symbolic Regression implementation based on Prioritized Grammar Enumeration (1), not Evolutionary or Genetic Programming. It produces a deterministic ...
- 179
7
votes
Accepted
Learning parameters of noise and filter coefficients from data where data and noise both have Gaussian distributions
So the way I went about formulating the problem was to essentially write the following equations:
The state that will be estimated, which is defined as a column vector, is the following:
$$w = [vec(A)...
- 3,778
7
votes
Accepted
When training a neural network, why choose Adam over L-BGFS for the optimizer?
This topic has been discussed at some length on Cross Validated (aka stats.stackexchange) and Reddit:
Why is Newton's method not widely used in machine learning? (see in particular Nick Alger's ...
- 2,136
7
votes
Accepted
What are the benefits of using machine learning for interpolation over traditional interpolation methods?
First of all, interpolation and approximation are slightly different from each other.
Given a sufficiently smooth function $f$ (sufficiently smooth just means that I am covering my bases, there are ...
- 2,321
7
votes
Why aren't Krylov subspace methods popular in the Machine Learning community compared to Gradient Descent?
They aren't popular because they don't work.
Nicol N. Schraudolph spent a few years on Krylov-like methods for Machine Learning. I first learned of his work at 2004 Machine Learning Summer School in ...
- 1,607
6
votes
Accepted
Artificial Intelligence, Modeling and Simulation
So bottom line is I don't see any comprehensive work on the use of AI in M&S as a whole, let's say having models that can learn how to produce new improved models using the existing models.
There'...
- 12k
5
votes
Why am I not seeing faster neural network training after upgrading to a vastly better GPU?
I suppose, you right and your network is not that big to 100%-utilize the GPU. The bottle-neck here seems to be not the GPU itself, but the transfer rate between RAM and VRAM and here the difference ...
- 114
5
votes
Accepted
Machine Learning for Optimization
The general idea that you have of learning an easy to compute model from results of your detailed simulation model and then optimizing the easy to compute model is long-established. The easy to ...
- 18k
5
votes
Accepted
Advantage of diagonal "jitter" for numerical stability?
So, you want to invert your matrix $A=\Phi^T\Phi$. For $A$ to be invertible it must not have zero eigenvalues. We can show that $A$ is positive semi-definite as follows. Positive semi-definite means ...
- 609
5
votes
Faster Logistic Function
If only low-accuracy approximations are needed, it is highly advisable to perform all computation in single precision, for example IEEE-754 binary32 format, usually ...
- 1,330
4
votes
Seeking a free symbolic regression software
I once started writing anopen source version of Eureqa in Java. The project has limited capabilities but it implements the fitness function described in [1] and couple optimizations mentioned by the ...
- 41
4
votes
Advantage of diagonal "jitter" for numerical stability?
Think of the simplest case when $\Phi$ is a scalar value.
Not well defined:
$$ \boldsymbol \theta^\text{ML} = (0^T 0)^{-1}0^T ~ y = \frac{1}{0} 0~y= \frac{0}{0} $$
Well defined:
$$ \boldsymbol \theta^...
- 817
4
votes
Advantage of diagonal "jitter" for numerical stability?
Look up something on Tikhonov regularization, also known as ridge regression in machine learning. This is a standard technique (but I agree that the explanation in that notebook is somewhat poor).
...
- 9,666
3
votes
Learning computational science through guided discovery
I learn computation science through Practical Numerical Methods with Python.
https://github.com/numerical-mooc/numerical-mooc/wiki
It covers finite differencing and many other numerical algorithms. ...
- 327
3
votes
Seeking a free symbolic regression software
I found the gramEvol R package flexible and easy to use.
They have a small tutorial in which they rederive Kepler's third law from data.
Note that it relies on Genetic Programmic for its optimisation ...
- 131
3
votes
Interpolation of Data Value using Optimized Weighting of Its Features
The problem is not convex, as one can verify using the simplest possible choice: $N=2, d=1$ and with data $x_1=x_2=1, f_1=1, f_2=0$. In that case, your objective function is
$$
F(C) = 2\left(1-\exp(-...
- 52.2k
3
votes
Accepted
Why is FLOP(Floating Point Operations Per Second) mentioned as a specification on every GPU?
This metric is pretty much as misleading (or useful, depending on your perspective) for GPUs as it is for CPUs.
Currently, a lot of applications/algorithm's implementations are limited more by memory ...
- 8,521
3
votes
Accepted
Interpolation vs. Neural network
I have limited experience in machine learning; however, simplifying, you can think of it as a "trained black box". I would say, you have to know a lot about your problem, the behaviour of your ...
- 8,521
3
votes
How to filter customer voice from customer - agent conversation recordings?
This seems to be the "Cocktail Party Problem". Andrew Ng's machine learning course on Coursera gives a solution based on SVD for this problem. See the first week's course notes. Ng refers to ...
- 609
3
votes
Accepted
Does the loss function in a deep neural network act as a norm?
Connection between Mean squared error and $L_2$ norm:
First the $L_2$ norm of a vector $\boldsymbol{x}\in\mathbb{R}^n$ is defined as
\begin{align*}
\lVert \boldsymbol{x}\rVert_2=\left(\sum\limits_{i=1}...
- 439
3
votes
Accepted
What problems does softmax() solve and when should I think of using it - in simple terms
Suppose you are training a neural network to predict the probability that a given picture is a picture of a cat, dog or tiger. This is an example of a problem called multi-class classification. The ...
- 609
2
votes
Seeking a free symbolic regression software
There is also a package for R called rgp. Visit this link.
https://cran.r-project.org/web/packages/rgp/index.html
I have not used rgp as I have only begun to use R seriously but it seemed like a ...
- 21
2
votes
fmincg implementation in Python
I assume you didn't specify the fprime parameter. If you don't provide this param fmin_cg has to figure out its own solution ...
- 121
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