Of course sine can appear in the solution for dynamical systems but the function itself is not dynamical. When evaluating sin(x) you do not need to know about the previous state.
Periodic function like sin(x) are not a dynamical system so its previous state does not determine the current state. So it should be approximated in that way.
This does not appear to be the usual approach of training the neural network on tons of data from the physics simulation. Instead they use the actual physics equations to form the loss function, which is a far more robust way of creating such an emulator. So physics based deep learning title is appropriate.
That really resonated with me. I basically stopped using Twitter because of the reasons you outlined here. This tool, however, might make Twitter useful again for me!
From the actual journal article: "Three further points are relevant to the question of whether the model-observed differences in
Figs. 10A-C are mainly due to underestimated observed tropospheric temperature trends or to an
overestimated satellite WV trend. First, independent estimates of tropospheric temperature change
from GPS radio occultation (RO) and radiosondes suggest that over the 2002 to 2018 period
of overlap between MSU/AMSU and GPS-RO, tropospheric warming is smaller in microwave
sounders than in GPS-RO or radiosondes (Steiner et al. 2020). Second, there is some evidence
that observational uncertainties may be smaller in satellite WV data than in satellite tropospheric
temperature data (Wentz 2013; see Section 2c). Third, when the individual trend components of
our four trend ratios are examined, the agreement between models and observations is better for
WV and SST trends than for TMT or TLT trends. These three lines of evidence, taken together with
the results of the RSS sensitivity tests, suggest that underestimated observed tropospheric warming
is plausible. This inference is predicated on the assumption that the model-based covariance
constraints are realistic."
The radiation is not pointed in the same direction as jets like a laser. There is bulk motion of the plasma in a given direction, but the radiation is emitted from particles that are moving in a different directions within that plasma. So the radiation spread is wider than the jet direction. Interestingly, depending on if the jet we are viewing is pointed towards us or not can impact on the radiation signature in the form of blue shift and red shift. If the orientation is just right, bits of jet appear to move faster than to the speed of light, but it's just a geometric effect.
There has been lost of theories to explain how jets from black hole systems form. New observations of light polarization from M87 jet show twisting magnetic field lines which suggest one of the theories might be right. That theory says that spinning black hole's energy can be extracted by these twisting magnetic field lines and therefore power these jets.
That's just one of the jets. In fact, I think only one side is observable as it pointed close to our direction, making the other side very difficult to observe.
Not all vaccines work the same way and it is not obvious what the long term impact of such a "flu pill" would be on our immune system. For example, I would like to know what would be the long term impact on children who do not get exposed to common colds while they are young. Would they go on to develop more autoimmune diseases. They might not, but it is a pretty big unknown.
That's true, I keep forgetting about https://lfortran.org/ Unfortunately in my experience the people I know who almost exclusively code in fortran are not really interested in jupyter notebooks.
It depends on what you are doing. If it is numerical work with matrix operations, then Fortran is fast and pretty intuitive. Some of the annoyances come from dealing with legacy code and mixing it with modern standards.
I am all for vaccines for really dangerous diseases, but we also need to get ill to keep our immune system active and healthy. For example, there are links between being in too clean an environment as a baby and then developing leukaemia. There is similar evidence for other autoimmune diseases.
Regarding dynamical systems, Neural ODEs hold promise as they are more analogous to the numerical solvers. I think with any dynamical system, purely data driven approach can be problematic because, as you say, the standard NN architectures are not great for it. You can however add physical constraints, e.g. minimize the Lagrangian as the objective function, to bring stability to these NN emulators.
There are some complex dynamics that take place when mass transfer is happening. In these systems this is via Roche Lobe overflow (1) which depending on the masses of the objects can become unstable after a large mass transfer. But going back to your original point, I guess there may be some configuration that leads to what to you are suggesting. Might be an interesting thing to model to see if it is possible!
Yes, they would gain mass from feeding but not get 40% bigger while still in that binary configuration. So it seems these BHs start out bigger than previously assumed.