6 ms·

Agreed that chaotic behavior shows up in unexpected places, but I'd still find it hard to believe here. What kind of state variable could show a sensitivity lik

Agreed that chaotic behavior shows up in unexpected places, but I'd still find it hard to believe here. What kind of state variable could show a sensitivity like that? If they're stuff like numbers of people, then at most they're going from one to the full population, many of orders of magnitude less than a double mantissa. And I'm not sure I'd be totally reassured that the simulation is deterministic when run single-threaded in a single start, if they run it multi-threaded for real? How could you be sure the non-determinism multi-threaded is all from the RNG issue, and not from real bugs that show up only multi-threaded, like race conditions accessing shared memory? With some effort, it should be possible to make the multi-threaded simulation deterministic too. If you want to run the simulation in multiple starts, then you can make that deterministic by saving the final seed in the intermediate output file and restarting from that. I've seen stuff like that in other non-deterministic code, and I'd find it (a) an unreasonable degree of rigor to expect from random academic code, and (b) a quite reasonable degree of rigor to expect in code whose output helps make decisions determining the safety and freedom of billions of people. But (a) and (b) unexpectedly became one and the same, so here we are.

eesmith 6y ago
You are making what is sometimes called an "argument from incredulity". Just because you find it hard to believe doesn't mean it's true. This issue parallels the foundational story of chaos theory. Quoting https://en.wikipedia.org/wiki/Chaos_theory https://en.wikipedia.org/wiki/Chaos_theory : > [Lorenz] wanted to see a sequence of data again, and to save time he started the simulation in the middle of its course. He did this by entering a printout of the data that corresponded to conditions in the middle of the original simulation. To his surprise, the weather the machine began to predict was completely different from the previous calculation. Lorenz tracked this down to the computer printout. The computer worked with 6-digit precision, but the printout rounded variables off to a 3-digit number, so a value like 0.506127 printed as 0.506. This difference is tiny, and the consensus at the time would have been that it should have no practical effect. However, Lorenz discovered that small changes in initial conditions produced large changes in long-term outcome. At the very least it shows that it's easy for intuition to be wrong. Do you accept that "issues with random seeds and parallel floating point reductions are extremely widespread, and a great deal of science gets done with non-deterministic simulations", re-quoting Carmack? That holds with my own experience. You ask "How could you be sure the non-determinism multi-threaded is all from the RNG issue, and not from real bugs that show up only multi-threaded, like race conditions accessing shared memory?" You cannot. Rather, how can you be sure that any program is bug-free? The question is, can you be confident enough to use it to make policy statements? Eg, people use imperfect models all the time when making laws.
- tripletao 6y ago
  I'm familiar with the concept of chaos. I've also spent a certain amount of time solving DEs for money, and most were not particularly chaotic. My superficial understanding of Ferguson's model is that it's an extended SIR model, with different classes of patient with different behaviors, geographical grouping, etc. From my intuition, it doesn't seem like that kind of DE would be too chaotic, and I haven't seen anything in the literature to suggest otherwise (since when systems do become sensitive to limited arithmetic precision, it's common for practitioners to notice and report that, as they first famously did with the weather in your example above). Note that this sensitivity isn't usually just a numerical implementation detail. For example, it's one of the reasons why the weather is so hard to predict, because the physical effects that create the weather are extremely sensitive to the real physical initial conditions, which we can measure only with some uncertainty, typically much worse than our numerical precision. So when such behavior is present, modelers are usually aware that it is, since it has consequences well beyond floating point reductions. I haven't seen that discussed in any of Ferguson's papers, so I strongly suspect that floating point issues may prevent bit-exact results but do not explain the variation seen. But in any case, I think we agree that's probably not the biggest difference, and the biggest difference is probably random numbers in the wrong order? I typically attempt to determine whether a program is bug-free by testing it. That's harder when a program is non-deterministic, so people often include the ability to derive all pseudo-randomness from a fixed seed. It looks like Imperial College tried to do that here, but it didn't work. I agree that's not a flaw in the model, just something that makes it harder to prove that no flaws exists. Would you at least agree that in a perfect world, with unlimited resources, that's something you'd fix?
  - eesmith 6y ago
    Given your expertise in solving DEs for money, and knowledge of chaos theory, why did you earlier mention "Yes, you can get chaotic behavior solving certain PDEs and stuff" and seemingly exclude the ordinary differential equations which started chaos theory? We know that transmissions rates are not fixed. While R0 models the average, sometimes 1 person infects 100 other people, and sometimes no one is infected. These 100+ events are rare, but not extraordinarily rare. If it happens early in a simulation, then your simulated model will result in a higher growth than one where that event occurs later. So sometimes you'll have a large outburst early, and sometimes it will be delayed a week or two. > My superficial understanding of Ferguson's model is that it's an extended SIR model, with different classes of patient with different behaviors, geographical grouping, etc. From my intuition, it doesn't seem like that kind of DE would be too chaotic The paper "Impact of non-pharmaceutical interventions (NPIs) to reduce COVID- 19 mortality and healthcare demand" appears to be the one which has influenced many. It cites https://www.nature.com/articles/nature04795 https://www.nature.com/articles/nature04795 as the model used, which cites https://www.nature.com/articles/nature04017 https://www.nature.com/articles/nature04017 which gives a summary: "We constructed a spatially explicit simulation of the 85 million people residing in Thailand and in a 100-km wide zone of contiguous neighbouring countries. The model explicitly incorporates households, schools and workplaces, as these are known to be the primary contexts of influenza transmission .. Random contacts in the community associated with day-to-day movement and travel were also modelled." I expect that sort of agent-based modeling, by nature, to be chaotic, along the lines I outlined above. You write: "So when such behavior is present, modelers are usually aware that it is, since it has consequences well beyond floating point reductions. I haven't seen that discussed in any of Ferguson's papers" How many papers of his have you read? The paper I quoted from, https://www.nature.com/articles/nature04017 https://www.nature.com/articles/nature04017 , includes: "Multiple assumptions are inevitably made when undertaking preparedness modelling for a future emergent infection. Sensitivity analyses are therefore critical for assessing the robustness of policy conclusions. Here, critical assumptions not already discussed include (1) the ratio of within-place to community transmission, (2) the expected generation time, Tg, of a new pandemic strain (largely determined by the duration of viral shedding and therefore infectiousness), (3) the level of heterogeneity in individual infectiousness (for example, ‘superspreaders’20), (4) antiviral efficacy/take-up, and (5) the sensitivity and specificity of case detection during the control programme." You rhetorically asked "Would you at least agree that in a perfect world, with unlimited resources, that's something you'd fix?" That's a bogus argument. If I had that sort of unlimited resources there are many more things I would rather use it on than making this simulation be the way you want it to be. For one, the noise and induced chaos are certainly far less than which result from the uncertain input values to the program.

eesmith 6y ago

You are making what is sometimes called an "argument from incredulity". Just because you find it hard to believe doesn't mean it's true. This issue parallels the foundational story of chaos theory. Quoting https://en.wikipedia.org/wiki/Chaos_theory https://en.wikipedia.org/wiki/Chaos_theory : > [Lorenz] wanted to see a sequence of data again, and to save time he started the simulation in the middle of its course. He did this by entering a printout of the data that corresponded to conditions in the middle of the original simulation. To his surprise, the weather the machine began to predict was completely different from the previous calculation. Lorenz tracked this down to the computer printout. The computer worked with 6-digit precision, but the printout rounded variables off to a 3-digit number, so a value like 0.506127 printed as 0.506. This difference is tiny, and the consensus at the time would have been that it should have no practical effect. However, Lorenz discovered that small changes in initial conditions produced large changes in long-term outcome. At the very least it shows that it's easy for intuition to be wrong. Do you accept that "issues with random seeds and parallel floating point reductions are extremely widespread, and a great deal of science gets done with non-deterministic simulations", re-quoting Carmack? That holds with my own experience. You ask "How could you be sure the non-determinism multi-threaded is all from the RNG issue, and not from real bugs that show up only multi-threaded, like race conditions accessing shared memory?" You cannot. Rather, how can you be sure that any program is bug-free? The question is, can you be confident enough to use it to make policy statements? Eg, people use imperfect models all the time when making laws.

tripletao 6y ago
I'm familiar with the concept of chaos. I've also spent a certain amount of time solving DEs for money, and most were not particularly chaotic. My superficial understanding of Ferguson's model is that it's an extended SIR model, with different classes of patient with different behaviors, geographical grouping, etc. From my intuition, it doesn't seem like that kind of DE would be too chaotic, and I haven't seen anything in the literature to suggest otherwise (since when systems do become sensitive to limited arithmetic precision, it's common for practitioners to notice and report that, as they first famously did with the weather in your example above). Note that this sensitivity isn't usually just a numerical implementation detail. For example, it's one of the reasons why the weather is so hard to predict, because the physical effects that create the weather are extremely sensitive to the real physical initial conditions, which we can measure only with some uncertainty, typically much worse than our numerical precision. So when such behavior is present, modelers are usually aware that it is, since it has consequences well beyond floating point reductions. I haven't seen that discussed in any of Ferguson's papers, so I strongly suspect that floating point issues may prevent bit-exact results but do not explain the variation seen. But in any case, I think we agree that's probably not the biggest difference, and the biggest difference is probably random numbers in the wrong order? I typically attempt to determine whether a program is bug-free by testing it. That's harder when a program is non-deterministic, so people often include the ability to derive all pseudo-randomness from a fixed seed. It looks like Imperial College tried to do that here, but it didn't work. I agree that's not a flaw in the model, just something that makes it harder to prove that no flaws exists. Would you at least agree that in a perfect world, with unlimited resources, that's something you'd fix?
- eesmith 6y ago
  Given your expertise in solving DEs for money, and knowledge of chaos theory, why did you earlier mention "Yes, you can get chaotic behavior solving certain PDEs and stuff" and seemingly exclude the ordinary differential equations which started chaos theory? We know that transmissions rates are not fixed. While R0 models the average, sometimes 1 person infects 100 other people, and sometimes no one is infected. These 100+ events are rare, but not extraordinarily rare. If it happens early in a simulation, then your simulated model will result in a higher growth than one where that event occurs later. So sometimes you'll have a large outburst early, and sometimes it will be delayed a week or two. > My superficial understanding of Ferguson's model is that it's an extended SIR model, with different classes of patient with different behaviors, geographical grouping, etc. From my intuition, it doesn't seem like that kind of DE would be too chaotic The paper "Impact of non-pharmaceutical interventions (NPIs) to reduce COVID- 19 mortality and healthcare demand" appears to be the one which has influenced many. It cites https://www.nature.com/articles/nature04795 https://www.nature.com/articles/nature04795 as the model used, which cites https://www.nature.com/articles/nature04017 https://www.nature.com/articles/nature04017 which gives a summary: "We constructed a spatially explicit simulation of the 85 million people residing in Thailand and in a 100-km wide zone of contiguous neighbouring countries. The model explicitly incorporates households, schools and workplaces, as these are known to be the primary contexts of influenza transmission .. Random contacts in the community associated with day-to-day movement and travel were also modelled." I expect that sort of agent-based modeling, by nature, to be chaotic, along the lines I outlined above. You write: "So when such behavior is present, modelers are usually aware that it is, since it has consequences well beyond floating point reductions. I haven't seen that discussed in any of Ferguson's papers" How many papers of his have you read? The paper I quoted from, https://www.nature.com/articles/nature04017 https://www.nature.com/articles/nature04017 , includes: "Multiple assumptions are inevitably made when undertaking preparedness modelling for a future emergent infection. Sensitivity analyses are therefore critical for assessing the robustness of policy conclusions. Here, critical assumptions not already discussed include (1) the ratio of within-place to community transmission, (2) the expected generation time, Tg, of a new pandemic strain (largely determined by the duration of viral shedding and therefore infectiousness), (3) the level of heterogeneity in individual infectiousness (for example, ‘superspreaders’20), (4) antiviral efficacy/take-up, and (5) the sensitivity and specificity of case detection during the control programme." You rhetorically asked "Would you at least agree that in a perfect world, with unlimited resources, that's something you'd fix?" That's a bogus argument. If I had that sort of unlimited resources there are many more things I would rather use it on than making this simulation be the way you want it to be. For one, the noise and induced chaos are certainly far less than which result from the uncertain input values to the program.