Edit: by predict the future, I mean predict every little event and it’s consequences in future, the human history and everything.
In: Physics
No, and this is a foundational principle of Chaos Theory.
In a non-linear dynamic system (even a system as simple as a [double pendulum](https://en.wikipedia.org/wiki/Double_pendulum)), even a tiny difference in the initial conditions will have a huge impact in how the system evolves over time, even if the system is fully deterministic. The [three-body problem](https://en.wikipedia.org/wiki/Three-body_problem) has been known about for a while.
An error in measurement will grow exponentially over time until the prediction is no better than if you had just put in the measurements at random (within the allowable values for the measurements). And because the error grows exponentially, how much your prediction improves doesn’t grow nearly as fast as how accurately you can measure the conditions. As the error goes to zero, how long the prediction is good for does not go to infinity, but to a finite value. And that’s before you throw in quantum mechanics, where the Heisenberg Uncertainty Principle puts a limit on how accurately you can measure something.
So if by predicting the future, you mean “predicting every little event and its consequences”, then no that’s not possible even in theory. And things like weather forecasts now take that into account. Rather than making one prediction, they make lots and lots of them with tiny little variations in each one and see how each plays out. The actual forecast is then more statistical in nature.
However, that doesn’t mean that predictions are entirely useless because some types of outcomes are more likely and some outcomes are impossible. With the three-body problem for example, if there are two large bodies and one small one, the most likely outcome is that the small body is ejected from the system.
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