Necessitarian and dispositionalist accounts of laws of nature have a well-known problem with "global" laws like the conservation of energy, for these laws don't seem to arise from the dispositions of individual objects, nor from necessary connections between fundamental properties. It is less well-known that a similar, and arguably more serious, problem arises for dynamical laws in general, including Newton's second law, the Schrödinger equation, and any other law that allows one to predict the future from the present.
The problem is not new. The underlying point is expressed nicely by Simon Blackburn in "Hume and Thick Connexions" (1990), where it is attributed to Hume:
[S]uppose we grant ourselves the right to think in terms of a thick connexion between one event and another: a power or force whereby an event of the first kind brings about events of the second. Nevertheless there is no contradiction in supposing that the powers and forces with which events are endowed at one time cease at another, nor in supposing that any secret nature of bodies upon which those powers and forces depend itself changes, bringing their change in its wake. Hume emphasises this point in both the Enquiry and the Treatise. (p.242)
A little later:
Equally if the 'nature of matter' is to help, it must also be so that the continuation of matter is not just one more contingency. (p. 244)
Let's make explicit how this applies to dynamical laws. Such laws narrow down the possible futures of physical systems, ideally (if they are deterministic) to a single possibility. Let's say we have a law according to which state S1 at time t1 will lead to state S2 at time t2. And suppose the world at t1 is full of non-Humean whatnots: relations of necessitation, fundamental dispositions, Aristotelian forces, or whatever. It seems perfectly conceivable that all these things either change or simply disappear between t1 and t2. So the presence of the non-Humean whatnots is compatible with many different futures. And so these whatnots cannot ground the dynamical law which reduces the number possible futures to one.
If this argument is sound, it not only means that the non-Humean accounts in question fail to capture the most important laws of science, but also that they fall prey to what is often claimed to be the main disadvantage of Humean accounts: to offer no explanation for the regularity of the world. If the presence of non-Humean whatnots at any point of time allows for many radically different futures, the dynamical regularity of the world can't be explained by the presence of these whatnots.
We need to have a closer look at the central premise in the above argument, that the presence of the non-Humean whatnots at a given time does not fix what is going to happen later.
Arguably, the premise is more plausible for some whatnots than for others. Philosophers who like primitive laws might object that these laws are not things that are "present" at a particular time and possibly absent or altered afterwards. Perhaps laws do their governing from outside time. So this view may be safe from the problem, although I would feel a little uneasy to stipulate that it's absolutely impossible for the basic laws of nature to change.
The problem is more acute for necessitarianism a la Dretske-Tooley-Armstrong and for the recently fashionable movement of dispositionalism.
On the Dretske-Tooley-Armstrong view, one might insist that the second-order necessitation relation between universals is atemporal and so couldn't possibly change. (Again, this would put an absolute ban on changing laws.) But the supposed atemporality of necessitation is arguably at odds with the contingency of this relation (as Helen Beebee points out in "Necessary Connections and the Problem of Induction" (2011), pp.511f.). Worse, it is hard to see how atemporal necessitation relations between universals could rule out the possibility of alien "invaders" (from Handfield 2001): new objects with new properties that suddenly appear out of nowhere. But deterministic dynamical laws rule out that possibility.
For dispositionalism, the problem is explored in some detail in Matt Tugby's "The problem of retention" (forthcoming), as well as pp.522f. of Beebee's paper, although neither of them explicitly considers the issue of dynamical laws. Here the central premise is especially plausible. The dispositionalist's non-Humean whatnots are fundamental dispositions. So our premise asserts that from the instantiation of certain dispositions at a certain time alone one cannot infer what is going to happen at later times. That seems right. To make such inferences, we need further assumptions about the temporal stability of these dispositions, of the objects that carry them, and about the absence of invaders. For example, the mere fact that an object has a certain mass at a given time doesn't entail that the object still exists at a later time, let alone that certain other objects won't exist at that time.
To get around the problem, dispositionalists would have to postulate a special kind of fundamental essential property that somehow guarantees a particular future evolution. Most simply, they could say that the present state of the world is essentially such that its future will be so-and-so. Alexander Bird mentions something like this in "The dispositionalist conception of laws" (2005) as a way of accounting for Principles of Least Action:
It might be that the intrinsic properties of the initial state make only one evolution possible, thanks to the dispositional essences of those properties. (p.367)
But notice, first, that ordinary intrinsic properties present in the initial state -- the distribution of mass, charge, spin, etc. -- do not suffice. (As we saw.) We would have to postulate new fundamental properties that look nothing like mass or charge or spin. The property I suggested, of being essentially such that the future will be so-and-so, isn't even dispositional in any meaningful sense.
Second, postulating such properties is intuitively implausible and ad hoc. Dispositionalism draws much of its popularity from the intuitive appeal of saying that a property couldn't be mass if it didn't behave like mass. But now it turns out that what does most of the metaphysical work (in grounding dynamical laws and ensuring the regularity of the world) is an entirely different claim that has no comparable pull: that the present physical state of the world couldn't exist unless the future is so-and-so.
Third, even if we grant that certain facts can be explained by appeal to the essence of the objects that are involved, explanations of this kind aren't automatic. For example, suppose we ask why Kripke became a philosopher. (Another dynamical question.) Suppose somebody answers that Kripke is essentially a philosopher. That is, Kripke is essentially such that he would eventually become a philosopher. Set aside whether this essentialist hypothesis is plausible in itself. (From a Lewisian perspective on essence, it is fine, in a suitable context.) Is it a good answer to my question? I'd say not. The answer doesn't shed any real light on how or why Kripke became a philosopher. Similarly, I think, for the supposed fact that the present state of the world is essentially such that the future is so-and-so: this doesn't really explain why the world evolves the way it does.
Finally (but relatedly), the whole idea of trying to get around the problem by postulating newfangled essential properties assumes that the problem is one about "metaphysical" modality: that we're merely looking for something that rules out metaphysically possible alternative futures. But it's not at all clear that our problem is a problem about metaphysical possibility. If one holds that the actual world is the only metaphysically possible world, would that put to rest the question why the world is regular, or what its dynamical laws are? I don't think so. Our dynamical laws don't just rule out metaphysically possible futures, they also rule out merely epistemically possible futures.
So the problem looks serious. I'm surprised that it is so little discussed.