So as the title implies, I really like playing games that allow you to take your time and slowly conquer the entire map. Far Cry 3-6, Halo Infinite and any Just Cause games or my current favorites. What are your favorites???

Basically, I have a simple dataset with one input and one output that I would like to perform nonlinear neural network regression on. Here is what it looks like:

https://preview.redd.it/poz9cuagg9c81.png?width=767&format=png&auto=webp&s=760fd608c652dc2c86b60cbb5a6d9e2a05a8196c

When I make a neural network in Keras with a ReLU activation function, no matter what I try with hidden layers and such, the model performs linear regression (even though this dataset is clearly not linear). I am aware that ReLU is a piecewise linear function, but it is nevertheless nonlinear. When I use sigmoid, the R^2 score increases significantly and the model more correctly models a nonlinear relationship. What can explain this? If ReLU is so successful compared to other activation functions, how can it not perform simple nonlinear regression that sigmoid performs effectively? Also, if I want to perform nonlinear regression, is using ReLU not an option? Thanks in advance!

I am looking for theory + steps for code + material constitute models.

Thank you

Hi, as the title says, I’m trying to plot a regression plane for a nonlinear model consisting of one response variable and two regressors, estimated via nls(). I tried using scatterplot3d but it doesn’t seem to work like for linear models. Is it possible to do it?

Looks like a pay wall to read the full article

Once again, quantum physics is telling Newtonian physics to go fuck right off. I swear, every few months there are new theories and/or new confirmations in quantum mechanics, and every few months I quietly re-evaluate what I think the Phenomenon could possibly be....

https://www.scmp.com/news/china/science/article/3157459/subatomic-level-past-can-be-future-quantum-researchers

"Conventional theory that time can only move forward challenged by study, but the conditions for a ‘backward arrow’ are limited."

Hi everyone. For a dataset consisting of three quantitative variables, H, M and W I have to build a non linear model of this form: E(H)=b0+b1M+(W/(b3+b4M)).

I tried using the "nls()" function in R, but I don't know how to determine the start values of the coefficients, b0, b1, b3 and b4. How can they be determined?

Hello, Let x(t) be solution of the x'(t) = f(x(t)), with initial conditions x(0) = x0, assume f being Lipschitz, so that existence and uniqueness of x(t) is guaranteed.
Now consider y(t) be solution of the y'(t) = f(y(t)) + e, with same initial conditions y(0) = x0, and e > 0 is some positive constant vector.
So can we say that y(t) > x(t) for all t > 0 ?
Also if e < 0 can we say that y(t) < x(t) for all t > 0 ?

Edit: inequalities are element-wise

So I picked up this game a few days ago, really enjoying it so far. Lily is so cute, love her swishy skirt. I've got the coven music stuck in my head, and Dark Witch Eleine was amazing.

I'm curious to know whether this game is nonlinear. Seems like the game presented me with a choice at the crossroads where the path split. I took the lower path and found the Coven. Eleine took me like 5 tries, she was a neat challenge. Feel like I've explored everything i can so far except that high path. I'm about to start playing again, and I'm really curious to see what happens. I'll be really disappointed if I can't progress without the Witch's Bubble lol.

Just for posterity, here's what I've got so far:

Chapter 3 Level 20 Eleine, Siegrid, Cliffside Hamlet Youth, Fungal Sorcerer, Floral Sorceress 4 relic slots, soiled prayer beads, manisa's ring, ruined witch's book

How am I going so far?

Software is R. Basically, I’m predicting values with two models, one linear and the other one non linear. If I type: > predict(linear_model, newdata = predict_data, interval = “confidence”)

and

> predict(linear_model, newdata = predict_data, interval = “prediction”)

it gives me the predicted values with the linear model, however the same code with the nonlinear model instead of the linear one, only gives me the prediction without the confidence intervals and the prediction intervals. Is there a way to solve this?

Separable DEQ have been introduced to me as DEQ of the form

> df/dx = h(f)*g(x)

or

> df(x)/dx = h(f(x))*g(x) , exhaustively.

I have no problem recognizing that this DEQ is ordinary and of first order, but I am totally lost at the other two categorizations. (Are even all DEQs categorizable with homogeneity and linearity? My gut says yes but obviously I'm not recognizing them here)

Thank you!

What is the definition of nonlinearity in time series relating to economics/econometrics, how would you identify nonlinear time series and why would this be important?

I am assuming that it's pretty common to use linear models to forecast economic time series but if a specific time series has nonlinear behavior, how would one deal with it in terms of forecasting?

I like to watch ninety day behind the scenes, and I see that it airs on sundays at 8 pm, and yet other days during the week they air episodes and its says its new and its bonus scenes and stuff, and now im watching an episode that claims to be new and Ive never seen it and its airing at 10 pm on a friday? Why cant it just air when its supposed to instead of all this bs

I am reading chapter 12 in Taylor's Classical Mechanics on nonlinear mechanics and the driven damped pendulum.  At this point, we have our normal differential equation for the driven damped oscillator,

d^2 φ/dt^2 + 2β(dφ/dt) + ω_0^2 (sin(φ)) = γω_0^2 (cosωt)

but instead of making the

sin(φ) = φ

approximation, we will add another term from the Taylor series, so

sin(φ) = φ - 1/6(φ^3 )

Then we substitute in our old linear solution

φ(t) = Acos(ωt - δ)

After some algebra, we now have a term that includes

A^3 cos[3(ωt - δ)]

Then the book says:

**"Since the right side contains no terms with this [cos3x] time dependence, it follows that at least one of the terms on the left (φ, dφ/dt, or d^2 φ/dt^2 and in fact all three) must. That is, a more exact expression for φ(t) must have the form

φ(t) = Acos(ωt — δ) + Bcos3(ωt — δ)

with B much smaller than A."**

Why does this follow?  What are we trying to achieve here?  I thought maybe we want to make the cos3x term small, but when I expand out the EoM with this new φ(t), I still have a cos3x term with a big (A^3) amplitude and nothing that seems to cancel it appreciably.  Plus I have cos5x, cos7x, cos9x terms.

The book said if I understood chapters 1-11, I could follow this nonlinear chapter, but this seems to be assuming aspects of differential equations I am unfamiliar with.  What could I read about differential equations to set me up better for this?

Hey everyone,

I am interested in using R to do a portfolio variance minimization problem using nonlinear programming but I only seem to see packages for linear programming problems. Does anyone know of a package for nonlinear programs? Thanks! If there is a package in Python for this, please let me know as well.

In spirit of yesterday being a bones day, I put together a few visuals last night to show off something people might not always think about. Enjoy!

Let's pretend our goal was to approximate this function with data.

`cos(norm(x))` over `[-4π, 4π]`

To demonstrate how a neural network "makes a nonlinear function linear", here I trained a 32 × 8 multilayer perceptron with PReLU activation on the function cos(norm(x)) with a random uniform 10k points over the [-4π, 4π] square. The training was done with 1k steps of full-batch Adam (roughly, my own version of Adam). Here's the final approximation.

(8 × 32) PReLU MLP approximation to `cos(norm(x))` with 10k points

Not perfect, but pretty good! Now here's where things get interesting. What happens if you look at the "last embedding" of the network, what does the function look like in that space? Here's a visual where I've taken the representations of the data at that last layer and projected them onto the first two principal components with the true function value as the z-axis.

Last-layer embedding of the 10k training points for the MLP approximating `cos(norm(x))`

Almost perfectly linear! To people that think about what a neural network does a lot, this might be obvious. But I feel like there's a new perspective here that people can benefit from:

When we train a neural network, we are constructing a function that nonlinearly transforms data into a space where the curvature of the "target" is minimized!

In numerical analysis, transformations that you make to data to improve the accuracy of later approximations are called "preconditioners". Now preconditioning data for linear approximations has many benefits other than just minimizing the loss of your neural network. Proven error bounds for piecewise linear approximations (many neural networks) are affected h

*examples

For me, it is Nolan's Memento. I generally don't like movies that jump around in time unless there is a good reason for it, and that was the case with Memento. In fact, this was central to the story.

I asked one of my friends the same question and he said, Out of Sight. Also a good movie, but not a personal favorite. Anyhow, I figured ask the question here as well....

I have just released Gomez - a pure Rust library for solving nonlinear systems of equations.

• crates.io
• repository
• documentation

The goals are:

• Derivative-free methods so that users don't need to care about providing gradient or Jacobian. Methods that are based on Jacobian use finite difference technique that should be fine in practice.
• Application in real-world problems. For example, the library supports specifying variable bounds (useful if the variables have some physical meaning for instance). More advanced constraints are currently out of scope, but contributions for their support are welcome.
• Global convergence. Numerical algorithms are very powerful, but also sensitive to initial guesses. I would like to provide tools for helping to overcome this issue.
• Control over the process. Solvers implement a low-level, iterative interface (similar to argmin) and should provide many settings to tweak them.
• Performance.

Supported algorithms in the initial version:

• Trust region -- This is mostly dogleg method with Levenberg-Marquardt fallback when Jacobian is singular. From simple benchmarks and my experience, it seems to be comparable with GSL hybrids implementation, although I would like to extend the benchmark and fix some todos before making any specific statement.
• Cuckoo search -- This is a first attempt to help with the sensitivity to initial guesses mentioned above. Basically any global optimization algorithm has a potential to be helpful, but this particular algorithm worked quite well for me in the past.
• Nelder-Mead (simplex) -- This was just an experiment, not recommended in general.

My main focus in the future will be on the global convergence topic, I have some interesting articles that I want to try.

https://youtu.be/nr777jFCoqg

With the disruption of an internal reserve electron source condenser array driven through overdrive reaction by a subspace injection from the osseous induction manifold, it can cause this action which under normal configuration would cancel out.

The G2 excitatory accelerator resonator emits a 1x10 erg output, counteracting a radiative meta particle field from the delta induction emission chromatic emitters. The load-in threshold flow regulator augers, maintains an onsite lower dimensional exotic fluid conduits where most of it precipitates and the remainder of the vortices that are formed due to the field oscillation, are redirected back into the supra Q vacuole. This process is carried out by a low frequency, high intensity, kaleidoscopic pulse of meta particle nuclear fusion by the beta cortical addite-on reaction chamber.

The gradient nucleator chamber, generates an integral leak of symmetrically distributed, known and unobservable form factors throughout the internal quark-gluon particle framework. This allows for a controlled flow of meta particles in the centripetal force of which it's momentum is ejected into the quark-gluon thickened-subspace field. The counter force by the Q1 generator, is applied to reverse the resulting matrix phenomena and return back to a normal mass density state. The accumulator chamber acts as a bosonic equilibrium stabilizer for inverted space augmentation by photonic conversion to prevent subquantum degradation through subspace dissolution at all times.

The nonlinear injection, on layer maximum velocity reversal multisystem, is separated into primary and secondary components by the super-charged infuser clusters. Maximum counterforce thrust is produced in the condenser clusters of an actively producing meta particle field that accelerated towards a unidirectional path set for particles to reach light speed without causing a spontaneous decay by approaching relativistic speeds. The mass redistribution matrix regulator executes a necessary controlled skewing subquantum mechanics reversal, in order to direct trapped space-time subspaces back into superposition conditions that did not appear before the singularity injection cycle. This exponentially decreases dilatant degenerating spacetimes from rupturing into overlapped voids or render total extraction something less than what would otherwise be infinite and instead consume only a normal amount of energy, associating with its transformation into mass. Rotation is power

The Niklas Luhmann archive does a great job showing how all of the notes within a top-level thought are linked together in a linear fashion. For example, Note 1 in the archive (Unity) has 124 notes within it that all trace back to Note 1.

But what if I wanted to, for example, link an existing note within Note 1 to an existing note within Note 2 (see image, red line), or even link two nonlinear notes within the same top-level thought such as linking Note 2.2 to Note 2.1a1 (same image, green line)? In that case the notes to be linked are on completely separate chains. Is this kind of nonlinear linking supported by the Zettelkasten framework? Is this even necessary, or am I missing something?

If nonlinear links are desired, then as the Zettelkasten grows, how do you ensure that the previously-unrelated notes are actually being discovered so that they can be linked? Is that just a matter of time spent with the Zettelkasten, or does anyone know of a better way?

Link: Simple example schematic of nonlinear links

Hello,

I'm following a nonlinear control textbook and and I have the following:

(1) dx/dt = - (1+sin^2 (x) ) x

(2) x(t) = x(0) exp(- integral from 0 to t (1 + sin^2 (x(tau))) dtau

(3) abs(x(t)) <= abs(x(0)) e^(-t)

I genuinely have no idea how you go from 1 to 2 and from 2 to 3. I tried treating one as a separable equation and when I get to the integration part, I run into an issue because I need to know the answer to solve the integral.

Hello everyone,

I am trying to solve a set of coupled non-linear differential equations using ode45 but i am not getting the desired results. By desired results I mean, setting all the initial conditions to be zero and setting torques for both joints to be 0, there should be no change in coordinate or change in velocity of the manipulator in other words if you plot the solution of the ode. It should be a horizontal line parallel to the time axis. But this is not the case when I run the code. Given below are the set of equations that I am trying to solve numerically:

https://preview.redd.it/zhe6jlawgk981.png?width=1033&format=png&auto=webp&s=81f08680b9e08ab50a130ab283b3a5953e7d56f2

And this is the code that i am using to solve the above system :

function xdot = DynOde(t,y)

%% init constants;

m1 = 5;

m2 = 2;

a1 = 0.34;

a2 = 0.34;

g = 9.81;

T1 = 0;

T2 = 0;

x1dot = y(2);

x1ddot = (T1*a2 - 2*a2 - 2*a1*cos(y(3)) - a1*a2*g*m1*cos(y(1)) - a1*a2*g*m2*cos(y(1)) + a1*a2^2*m2*sin(y(3))*y(2)^2 + a1*a2^2*m2*sin(y(3))*y(4)^2 + a1*a2*g*m2*cos(y(3))*cos(y(1) + y(3)) + a1^2*a2*m2*cos(y(3))*sin(y(3))*y(2)^2 + 2*a1*a2^2*m2*sin(y(3))*y(2)*y(4))/(a2*(a1^2*m1 + a1^2*m2 - a1^2*m2*cos(y(3))^2));

x2dot = y(4) ;

x2ddot = (T1*a2 - 2*a2 - 2*a1*cos(y(3)) - a1*a2*g*m1*cos(y(1)) - a1*a2*g*m2*cos(y(1)) + a1*a2^2*m2*sin(y(3))*y(2)^2 + a1*a2^2*m2*sin(y(3))*y(4)^2 + a1*a2*g*m2*cos(y(3))*cos(y(1) + y(3)) + a1^2*a2*m2*cos(y(3))*sin(y(3))*y(2)^2 + 2*a1*a2^2*m2*sin(y(3))*y(2)*y(4))/(a2*(a1^2*m1 + a1^2*m2 - a1^2*m2*cos(y(3))^2));

xdot = [x1dot;x1ddot;x2dot;x2ddot];

end

Please let me know if I have written the correct vector field representation of the two equations in the picture.

Any advice would be of great help.

Thank you.

Hi everyone. For a dataset consisting of three quantitative variables, H, M and W I have to build a non linear model of this form: E(H)=b0+b1M+(W/(b3+b4M)).

I tried using the "nls()" function in R, but I don't know how to determine the start values of the coefficients, b0, b1, b3 and b4. How can they be determined?

Basically, I’m predicting values with two models, one linear and the other one non linear. If I type: > predict(linear_model, newdata = predict_data, interval = “confidence”)

and

> predict(linear_model, newdata = predict_data, interval = “prediction”)

it gives me the predicted values with the linear model, however the same code with the nonlinear model instead of the linear one, only gives me the prediction without the confidence intervals and the prediction intervals. Is there a way to solve this?

Basically, I’m predicting values with two models, one linear and the other one non linear. If I type: > predict(linear_model, newdata = predict_data, interval = “confidence”)

and

> predict(linear_model, newdata = predict_data, interval = “prediction”)

it gives me the predicted values with the linear model, however the same code with the nonlinear model instead of the linear one, only gives me the prediction without the confidence intervals and the prediction intervals. Is there a way to solve this?

Hi everyone. For a dataset consisting of three quantitative variables, H, M and W I have to build a non linear model of this form: E(H)=b0+b1M+(W/(b3+b4M)).

I tried using the "nls()" function in R, but I don't know how to determine the start values of the coefficients, b0, b1, b3 and b4. How can they be determined?

Hi everyone. For a dataset consisting of three quantitative variables, H, M and W I have to build a non linear model of this form: E(H)=b0+b1M+(W/(b3+b4M)).

I tried using the "nls()" function in R, but I don't know how to determine the start values of the coefficients, b0, b1, b3 and b4. How can they be determined?