Changing circuitry of analog computer *During* simulations?

[FactChecker]

Something like this ?

(Jump to 3:30 for the best bits)

This looks very interesting. (It took me a while to realize that the link was there and not missing.) I wonder if @Kirana Kumara P is familiar with how Mosegaard is doing that?

 

[Kirana Kumara P]

Something like this ?

(Jump to 3:30 for the best bits)

I was aware of this kind of simulations about ten years ago. This kind of simulation (using spring-mass systems) is decades old. I am not happy with the method (hence looking for better methods. "I am not happy" in the last sentence is not just a subjective opinion of just one person (me) but it is the opinion of the community who works in the area. Moreover, it is not just an opinion but a fact (which can be justified). Of course, the method is still useful for solving certain problems. I am very clear about my problem (I have got more than 300 standard references). Of course, I too would go for some approximation (maybe a new type of approximation) if the analog computer, ASIC, FPGA do not help. And I am capable of solving the problem by coming up with some new approximation and by using a digital computer. But the purpose of posting my question here in the forum is mainly to know whether the problem can be solved by using an analog computer.

 

[Baluncore]

But the purpose of posting my question here in the forum is mainly to know whether the problem can be solved by using an analog computer.

No, it can't be solved with an analogue computer.

 

[Kirana Kumara P]

A 1 litre organ will weigh about 1kg. 1 mm resolution in 3D will require about 1 million elements. You cannot realistically build an array of 1 million analogue computers so you have to switch analogue processors between elements or tasks in microseconds. That is simply not possible due to the cost of the analogue sample and hold storage arrays required, or the number of A–D and D–A converters needed to operate at video speeds of about 50 MHz in parallel.

It is enough if the organ is divided into about 1000 elements. That is why I told in one of my earlier replies that we could aim to solve a set of 5000 equations. These numbers (total number of equations in the set) are not just arbitrary numbers; I have arrived at these numbers by careful thinking and rough calculations (and also by cross-checking with the existing literature).

 

[Kirana Kumara P]

In an analog computer, the state variables are continuously available as a result of the continuous integrals, derivatives, and other signal values. They are continuous and have no frame time or sampling frequency..

In an analog computer (for our problem), if input is constant output will also be constant (after the elapse of the settling time). The input can be changed thirty times per second (or, every 30 milliseconds) so that the output will also change the same number of times. This itself is the frame rate (30 times per second) here.

 

[Kirana Kumara P]

Everything is an approximation. Just because a problem has not been solved to your satisfaction does not mean it is established as impossible. If that was the case, no problem would ever be solved.

Still people keep looking for better solutions. Otherwise digital computers would not have come into existence, if people were satisfied with analog computers (and did not try for a better system).

 

[FactChecker]

In an analog computer (for our problem), if input is constant output will also be constant (after the elapse of the settling time). The input can be changed thirty times per second (or, every 30 milliseconds) so that the output will also change the same number of times. This itself is the frame rate (30 times per second) here.

Any D-As can handle much higher input rates of change than 30 frames/sec. The internal workings of an analog computer are analog, continuous signals and have no "frame" times. Old mixed analog/digital flight simulations have run when analog computers were connected to digital inputs that were changing at 1000 Hz. Even then, the analog computer was capable of MUCH higher rates and the digital calculations were the limiting factor. Commercially available FPAAs can handle signals up to 2 MHz. When their results are plotted, the smoothness of them compared to equivalent FPGAs are obvious. (e.g see figures 9 and 10 of https://www.researchgate.net/publication/224597250_A_comparison_of_FPGA_and_FPAA_technologies_for_a_signal_processing_application )

 

[Kirana Kumara P]

Any D-As can handle much higher input rates of change than 30 frames/sec. The internal workings of an analog computer are analog, continuous signals and have no "frame" times.

I need the concept of frames because the biological organ is displayed on a monitor which is connected to a digital computer (the analog computer is coupled to that digital computer). In analog computers, I think the "frame rate" is limited by the settling time (time required to change the connections/parameters would also matter of course).

 

[Baluncore]

It is enough if the organ is divided into about 1000 elements. That is why I told in one of my earlier replies that we could aim to solve a set of 5000 equations. These numbers (total number of equations in the set) are not just arbitrary numbers; I have arrived at these numbers by careful thinking and rough calculations (and also by cross-checking with the existing literature).

I believe a 5000 equation system can be solved now on an array of digital processors or on a multi-GPU board in a PC. With the advent of arrays of 1024 digital processors on a chip, there is no way that next year, anyone will be satisfied with only 1000 elements. You must now be designing a solution that will be up-to-date in 3 to 5 years time.

Storing 5000 state variables in capacitors with 5000 op-amps and 5000 multiplexors will be more expensive and much less flexible than storing those variables digitally in the memory provided on-chip with a RISC processor array.

The problem you describe cannot be economically solved with an analogue computer array. Any wishful thinking that it can be economically solved with an analogue computer is becoming more paralogical by the hour.

 

[FactChecker]

I need the concept of frames because the biological organ is displayed on a monitor which is connected to a digital computer (the analog computer is coupled to that digital computer). In analog computers, I think the "frame rate" is limited by the settling time (time required to change the connections/parameters would also matter of course).

No. There is no "frame rate" in an analog computer. It is responding to the step inputs as the continuous differential equations of the system modeled would respond to such inputs. If you could run your inputs at a much higher rate, the inputs would just have much smaller steps and the results from the analog computer would be more accurate. So the analog part would respond as the real organ would if your poking motions were in steps of 30 Hz. Any problems are not due to the analog computer; they are due to the rough, steps of the inputs.

PS. Insisting that the computer "settle" in for each new input is incorrect. The actual process of poking an organ would behave in a smoother way. You don't want rough 30 Hz steps to be passed through in an unnatural way. Ideally, you would either change your inputs at a faster rate or smooth out the results with some filtering (but that would have to be done carefully).

 

[FactChecker]

I don't know if this discussion about the response of analog computers is beneficial to you. I really don't see how you can make it adapt to the changes that you need in a simulated operation. But maybe others have some ideas.

 

[Kirana Kumara P]

I
Storing 5000 state variables in capacitors with 5000 op-amps and 5000 multiplexors will be more expensive and much less flexible than storing those variables digitally in the memory provided on-chip with a RISC processor array.

Even if the analog storing is more expensive and less flexible, if it could be faster then still one could think of them (of course, I have taken note of the concerns raised in several of the replies, over the use of analog computers). Of course I would prefer a digital computer (can try RISC also) if there is no advantage going for an analog computer.

I
The problem you describe cannot be economically solved with an analogue computer array. Any wishful thinking that it can be economically solved with an analogue computer is becoming more paralogical by the hour.

If "economically" refers to speed (in comparison to a digital computer) then no one would prefer an analog computer. If "economically" refers to cost, someone may try it at least in principle; some may not worry about the future use if they are convinced that there is advantage (in terms of speed) going for an analog computer at present.

 

[Baluncore]

An analogue computer in this application is a low pass filter. If there are no changes it will settle exponentially towards a final value. That says it will never actually settle, but always be on a trajectory towards a closer solution. The frames that are considered for the display will be samples of the state variables at the specified times, but it is important that the process be allowed to continue without interruption by the data sampling that creates the frames.
The implementation of IIR digital filters has the same topology as the analogue computer elements being considered here to solve the equation set.

If "economically" refers to cost, someone may try it at least in principle; some may not worry about the future use if they are convinced that there is advantage (in terms of speed) going for an analog computer at present.

Only a steampunk fanatic would attempt to build an analogue computer to simulate surgery. They would not succeed.

 

[Kirana Kumara P]

No. There is no "frame rate" in an analog computer. It is responding to the step inputs as the continuous differential equations of the system modeled would respond to such inputs. If you could run your inputs at a much higher rate, the inputs would just have much smaller steps and the results from the analog computer would be more accurate. So the analog part would respond as the real organ would if your poking motions were in steps of 30 Hz. Any problems are not due to the analog computer; they are due to the rough, steps of the inputs.

PS. Insisting that the computer "settle" in for each new input is incorrect. The actual process of poking an organ would behave in a smoother way. You don't want rough 30 Hz steps to be passed through in an unnatural way. Ideally, you would either change your inputs at a faster rate or smooth out the results with some filtering (but that would have to be done carefully).

To avoid confusion, let us not use the word "frame" when it comes to analog computing. All I am interested in is to get the solution within 30 milliseconds. The steps that you have mentioned may refer to how the input is applied. I am interested only in the final value of the input (or the final step). Of course we would use sufficient number of steps so that the result for the final step is acceptably accurate. Once the result for the final step is known, then I would transfer the final result alone (not the results for the intermediate steps) to the digital computer which would display the result on the screen connected to it. It should be possible to get the solution for the final step within 30 miliseconds.

Next, I would change the connections and/or parameters, and run a similar simulation as above again, and again transfer the final result to the digital computer. Again I would transfer only the result for the final step here (I am not interested in the intermediate steps here also). The entire process mentioned in this paragraph should be over within 30 milliseconds.

The tasks mentioned in the last paragraph would continue for the entire duration of the simulation of biological organs (for half an hour, say).

Now the digital computer receives about 30 results per second for the entire duration of the simulation, and it renders the results on the screen. there will be visual continuity since there are about 30 frame per second now.

 

[FactChecker]

To avoid confusion, let us not use the word "frame" when it comes to analog computing. All I am interested in is to get the solution within 30 milliseconds. The steps that you have mentioned may refer to how the input is applied. I am interested only in the final value of the input (or the final step). Of course we would use sufficient number of steps so that the result for the final step is acceptably accurate. Once the result for the final step is known, then I would transfer the final result alone (not the results for the intermediate steps) to the digital computer which would display the result on the screen connected to it. It should be possible to get the solution for the final step within 30 miliseconds.

I understand. I don't want to get hung up on something that is probably of no benefit to you (because I don't think that analog computers are right for your task), but I can't resist making one last point. The actual physical object would react to the changed input in some smooth way that is determined by differential equations. The analog computer will mimic that in a continuous way. It accurately represents the real physics at every point in time, not just at the end of the 30 Hz frames.

 

[Kirana Kumara P]

The analog computer will mimic that in a continuous way. It accurately represents the real physics at every point in time, not just at the end of the 30 Hz frames.

But the problem definition does not specify how the input varies within 30 milliseconds (input is constant). Once the problem is clearly defined, that definition of the problem would be the true physics (although the reality can be slightly different). Anyway, the very final result is the image that is manipulated on the screen, and that depends only on the value of the final step. Then the use of the intermediate steps would be just a way to address the nonlinearity present in the system.

 

[FactChecker]

But the problem definition does not specify how the input varies within 30 milliseconds (input is constant). Once the problem is clearly defined, that definition of the problem would be the true physics (although the reality can be slightly different). Anyway, the very final result is the image that is manipulated on the screen, and that depends only on the value of the final step. Then the use of the intermediate steps would be just a way to address the nonlinearity present in the system.

Right. My point is that there is no concern about "settling time" and frame rates inside the calculations of the analog computer. All the signal values and states are correct for the given differential equations and input signals at all times. That can greatly reduce the problems of synchronizing computer operations and minimizing latency.

 

[Nidum]

Games , FX and lateral thinking .

Physics engines

 

[Kirana Kumara P]

Games , FX and lateral thinking .

These systems (e.g., particle systems) are usually used in computer games and the accuracy offered by them is poor. It is okay to use them for gaming since there it is enough if the simulations "look" realistic. They are usually a very crude approximation of the true physics. They are not usually used for engineering analysis. The accuracy can improve when these types of systems employ methods like the finite element method, but even when this happens to be the case, bad finite elements (low accuracy) are deliberately used to achieve faster simulations, as has been done in the above link. Of course, it may serve their purpose, but it will not serve our purpose.

Again, I have been aware of this type of simulations since long time.

 

[Baluncore]

Next, I would change the connections and/or parameters, and run a similar simulation as above again, and again transfer the final result to the digital computer. Again I would transfer only the result for the final step here (I am not interested in the intermediate steps here also). The entire process mentioned in this paragraph should be over within 30 milliseconds.

Your misunderstanding of analogue computers explains your weird approach and the title of this thread. You are treating the analogue computer as if it is a discrete multi-tasking digital computer running fixed-time algorithms. It is in fact a continuous function of continuous inputs. There can be no final step in an equation solution as the state variables will never really be stable. The output of an analogue processor that you display will be the result of a low-pass filtering process of the recent values of state variables. You cannot afford to wait for the solution to settle, nor can you waste time reloading the state variable values, or restarting the circuit for every frame.

 

[Kirana Kumara P]

Your misunderstanding of analogue computers explains your weird approach and the title of this thread. You are treating the analogue computer as if it is a discrete multi-tasking digital computer running fixed-time algorithms. It is in fact a continuous function of continuous inputs. There can be no final step in an equation solution as the state variables will never really be stable. The output of an analogue processor that you display will be the result of a low-pass filtering process of the recent values of state variables. You cannot afford to wait for the solution to settle, nor can you waste time reloading the state variable values, or restarting the circuit for every frame.

This could mean that an analog computer is infinitely fast. One gets the output (result) as soon as the input is applied. Am I right?

 

[Baluncore]

This could mean that an analog computer is infinitesimally fast. One gets the output (result) as soon as the input is applied. Am I right?

Probably not.
"infinitesimally fast" actually means so slow it appears to never change.
"infinitely fast" actually means so fast it appears to be instant.

The integrators take time to change. The immediate value will be whatever you initialise it with.
That would suggest that the immediate output is not the next state, but is actually the previous state.

 

[Kirana Kumara P]

Probably not.
"infinitesimally fast" actually means so slow it appears to never change.
"infinitely fast" actually means so fast it appears to be instant.

The integrators take time to change. The immediate value will be whatever you initialise it with.
That would suggest that the immediate output is not the next state, but is actually the previous state.

I had corrected it to "infinitely fast". What would be the typical time lag?

 

[Baluncore]

I had corrected it to "infinitely fast". What would be the typical time lag?

You must define what you mean by "time lag".
If the inputs did not continue to change, the Time Constant of the integrators would get it to within 37% of a theoretical final value. Two TC will get to within 13.5%, 3TC to 4.9%, 4TC to 1.83%, 5TC to within 0.67%...

 

[FactChecker]

You must define what you mean by "time lag".
If the inputs did not continue to change, the Time Constant of the integrators would get it to within 37% of a theoretical final value. Two TC will get to within 13.5%, 3TC to 4.9%, 4TC to 1.83%, 5TC to within 0.67%...

In modeling a physical process in time, there should be no integrators, filtering, or signal latency except those that model the real physical process. There are no "final values", there are just the correct values as a function of time.

 

[FactChecker]

This could mean that an analog computer is infinitely fast. One gets the output (result) as soon as the input is applied. Am I right?

Yes. You should instantly get the result that the physical process would have at that time, given the same inputs in time. And the results should change with time as the physical process would. (After all, the analog computer is an electrical physical process made to mimic your problem.) I consider an analog process to be equivalent to a digital process with an infinitely small time step. There is no data latency internal to the analog computer.

Suppose you have a step input with steps every 33 milliseconds. An analog computer will instantly start to respond to the step changes as a physical process would. The step inputs are not realistic, because your real physics had a continuous analog input that went smoothly from the prior step value to the new step value. So the simulation has some delay due to the "sample and hold" nature of your inputs. The essential difference between the analog computer and a digital one is that the analog computer outputs will start to respond immediately whereas the digital computer will hold its output constant till it can compute new outputs (about 33 milliseconds later). Here I am assuming that the digital calculations would be done in a "hard loop" with as small a frame time as possible and that its new outputs would not be available till 33 milliseconds after the inputs change. The signal latency of the simulation may be compensated for with predictors (lead filters), but that will introduce noise which may not be acceptable. The results of the analog simulation can be improved by giving it inputs that are as close to continuous as possible (a higher rate than 30 Hz). That will not help a digital simulation unless it can run at the faster rate.

That being said, I do not see any way to set up an analog computer for your problem. You do not have a simple problem of switching between a small number of signal paths. Your simulation will have to adapt to far more situations than I have ever dealt with on an analog computer. I don't see how you could use analog computers, unless there are some massively parallel ones. And I am not aware of any.

 

[anorlunda]

@Kirana Kumara P , how many times do you need to be told, "No," before you accept the answer?

You should present your desires to your engineers and then accept their advice about what is feasible and how to go about it. If the situation were reversed and the engineer said to you, "Treat the patient with non-surgical methods," I'm sure you would quickly say "Leave the medicine to me."

 

[FactChecker]

@Kirana Kumara P , how many times do you need to be told, "No," before you accept the answer?

You should present your desires to your engineers and then accept their advice about what is feasible and how to go about it. If the situation were reversed and the engineer said to you, "Treat the patient with non-surgical methods," I'm sure you would quickly say "Leave the medicine to me."

Maybe he has accepted the answer and still has some intellectual curiosity on the subject. In my opinion this thread has been a little confusing.

 

[Baluncore]

In my opinion there has been some misleading information in this thread.

That is probably true of almost every thread as the OP question is rarely fully explained.

I believe this may be a case of the Dunning–Kruger effect; the experts are concerned with doubts and details that only they understand, while the OP does not understand the depth of the advanced technology, but continues to grasp for hope of a solution, long after Pandora's box has been well ventilated.

 

[FactChecker]

That is probably true of almost every thread as the OP question is rarely fully explained.

I believe this may be a case of the Dunning–Kruger effect; the experts are concerned with doubts and details that only they understand, while the OP does not understand the depth of the advanced technology, but continues to grasp for hope of a solution, long after Pandora's box has been well ventilated.

I would like to restate my post. I think the information has been correct, but maybe not exactly answering the right question. I reworded it to say that I think the thread has been a little confusing.

 

[Kirana Kumara P]

Some of the replies in the thread are clear that it will not be possible to build an analog computer that can solve the concerned problem, while the others worry about the complexity, cost, reliability, risk (probability of success), future use, possibility of not being able to come up with an (suitable) analogy/circuit etc.

I am not convinced still that it is not possible to build an analog computer that can solve the concerned problem. However, I am less likely to design/build the said analog computer, at least for the time being.

I would like to once again express my since gratitude to all those who have spent their precious time answering my questions.