[HN Gopher] Finding Paths of Least Action with Gradient Descent
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       Finding Paths of Least Action with Gradient Descent
        
       Author : E-Reverance
       Score  : 15 points
       Date   : 2025-04-26 06:24 UTC (16 hours ago)
        
 (HTM) web link (greydanus.github.io)
 (TXT) w3m dump (greydanus.github.io)
        
       | constantcrying wrote:
       | >Some, like the double pendulum or the three-body problem, are
       | deterministic but chaotic. In other words, their dynamics are
       | predictable but we can't know their state at some time in the
       | future without simulating all the intervening states.
       | 
       | Literal nonsense. Everything in the second sentence is false.
       | 
       | Deterministic means that the state at some point in time fixes
       | the state at all future points in time. Nevertheless in a
       | deterministic system you can know a future state without
       | calculating intermediary states.
       | 
       | Chaotic means that future states are discontinuous in regards to
       | the initial state. Nevertheless a chaotic system can be known at
       | future states without calculating intermediary states, you can
       | even have an _analytic_ solution to a chaotic system. Furthermore
       | chaotic can mean that you _can 't_ calculate future states from
       | initial states. Numerical ODE solvers in particularly have errors
       | which grow exponential in time. So simulating intermediate states
       | does not give you the solution to the problem.
        
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       (page generated 2025-04-26 23:02 UTC)