We are searching for ways to better sample the probability distribution of forecast uncertainty

look at using AI/ML to produce numerical weather prediction (NWP) forecasts – but with a twist, we would like to consider it for data assimilation, i.e. to initialize an existing numerical weather prediction system.



Our problem is that errors in the initial conditions of our forecast models are the main source of errors in our forecasts.

* To initialize our models we need to account for the uncertainty in all the information (the prior – which comes the previous forecast, and the new information – from observations)
* This uncertainty depends on the state of the atmosphere – which is what we are trying to find
* The uncertainty exhibits significant and important variation in space and time and between variables
* These relationships are important, as they must be consistent with the model relationships



To do this we use an ensemble, a set of different runs for the forecast model, that attempt to provide random samples for the probability distribution of the atmosphere, given all prior information. This is not only used to predict the uncertainty in the longer forecast but also to approximate the statistics of the error structure for our initialization

* This is a bit challenging when our models have around 10^9 or more degrees of freedom, to say the least

The big advantage is that the starting position is clear enough – train an ML scheme to duplicate a full NWP system.

For that we have huge data stores to act as training data

There are also several papers describing other efforts to do this



The difference is that instead of trying to go head to head with groups such as NVIDIA which are focussing on global prediction for days 2-7, we would like to focus on

* Just the next few hours (so need greater accuracy and better representation of spatial relationships), so can just initialize our ensemble for the next round of forecasts
* Would aim to increase the number of realizations in our ensemble

* So would need to generate full 3d fields (NVIDIA did not do a good job of that in their last paper)
* Would only need to be perturbations to the existing ensemble- so perturbations of perturbations, which may be less non-linear and more amenable to ML

Full forecasts with AI (but not quite what we need)
https://arxiv.org/abs/2202.07575
https://arxiv.org/abs/2202.11214

DefendTex designs, manufactures and assembles a range of semi-autonomous air vehicles or drones.

The product range includes;
Drone40: A nano class drone weighing approximately 250g depending on payloads. This drone can fly for 10 – 30 minutes and collapses down to a 40mm cylinder which is easy to carry on the person. The 40mm cylindrical format also allows it to be launched from a grenade launcher or pneumatic tube launcher system. This drone is used by individuals or launched from host vehicles including air, land and sea. Like all DefendTex drones the Drone40 is fitted with our internally developed and manufactured semi autonomous autopilot based on the Ardupilot eco-system of software and peripherals.
Drone81: This drone weighs approximately 3kg depending on payload configuration and can fly for up to 90 minutes. It is still quite portable and is most often used by people and not launched from other vehicles. The Drone81 features the DefendTex autopilot but also carries some serious compute hardware in the form of either Nvidia Jetson Xavier / Orrin NX CPU/GPU accelerator or an AMD/Xilinx Kria FPGA / CPU system.
Drone155: This drone weighs up to 25kg and is our heavy lift option. It can be used to move medical supplies or material such as water and food around the battlefield. It can fly for over 2 hours depending on payload config and weights anywhere between 5kg and 25kg fully fitted out. It also carries the DefendTex autopilot system and again features compute hardware similar to Drone81.
All of these drone systems are built from commodity components and designed to be as simple and as low cost as possible. The affordable and often disposable nature of DefendTex drone systems is what makes them unique and is core to their utility to our customers.
We face a range of problems ranging from the relatively mundane to the complex when it comes to operating these Drone systems in realistic environments. These problems fall into several broad categories, Localisation and Mapping, Swarming and Flocking and Distributed Decision Making and Path Planning.
Localisation and Mapping The DefendTex autopilot utilises a number of commercially available sensors commonly found in smart phones to understand the world and to fly semi-autonomously. These sensors include a 3 axis accelerometer, a 3 axis gyroscope, a 3 axis magnetometer, a multi constellation GPS module, a barometer and sometimes a laser range finding altimeter. The autopilot uses an extended Kalman filter to estimate the 3D position of the Drone based on the GPS location, the height above ground and the sensed inertial movement of the platform. The Kalman filter is essential to counteract the inherit inaccuracy in the process of double integrating acceleration to obtain position. The sensors used in smart phones and our drones are deliberately noisy due to international regulations on the accuracy of inertial measurement units. The Kalman filter monitors all the sensors and uses covariance to detect errors and discard noisy measurements. The GPS subsystem is chiefly responsible for detecting inertial measurement errors and as such when it is not longer working, due to jamming or drop outs, our Drones have great difficulty navigating their way. Commonly autonomous systems employ vision based solutions such as SLAM to navigate in places where GPS is not available. This is quite computationally intensive and not necessarily possible on small platforms like Drone40. We are very interested in novel solutions to GPS denied navigation and localisation that do not involve computationally intense methods like SLAM. A particular line of research has recently been identified in our own review of the literature that uses magnetometer anomaly as a source of structure that can be used to enable SLAM like algorithms without the use of high resolution cameras. This and other low compute methods of improving the accuracy of our inherently flawed inertial measurements are interesting problems.
Swarming and Flocking
A single drone is useful but a swarm is much more so. Our drones feature high bandwidth meshing WiFi based on IEEE 802.11s. We are able to use this network to share state of each drone in a swarm to each other drone. This can then be used to implement emergent behaviours such as swarming and flocking from reasonably simple rule sets. We are very interested in swarming and flocking algorithms and solutions that are resilient to intra-swarm comms loss and that also prevent potential collision with other swarm members.
Distributed Decision Making and Path Planning Controlling a large number of individual drones, if entrusted to a human operator, creates an onerous cognitive burden. It is preferable for an operator to describe a mission in terms of goals, outcomes or other measures and have the system, or swarm, determine how best to achieve those goals or outcomes. We are aware of several techniques that may deliver this outcome such as distributed decision making, job auctioning and consensus determination which may lead to this functionality.
Open Call
The above are areas we have thought about and have invested time seeking solutions. We are also keenly aware there is a large range of interesting things that can be done with low cost swarms of drones and are open to proposals for solutions to problems we have yet to think about. Please feel free to suggest approaches we have not directly discussed here.

How should a trader adjust her position when trading a mean-reverting instrument?

It is fairly straightforward to identify a financial instrument that mean-reverts in price.

Then, if the price is higher than the mean, the trader will sell the instrument (take a short position) and so will profit when it mean-reverts. Similarly, if the instrument falls below its mean, this will be an opportunity to buy the instrument (take a long position) and then wait for it to mean-revert.

Of course, traders are constrained by position limits. Let’s say that the size of a trader’s position in this instrument may be at most N units. Then, for example, if the instrument falls in value by a single increment and the trader buys N lots of this instrument, they will not be able to increase their position size if the instrument falls further. This strategy is clearly not optimal. Maybe they just want to buy a little bit and then wait further for a bigger opportunity before buying more. Or perhaps they only want to trade when the instrument is quite far away from the mean.

In short, how can we optimise the accumulation of a position so as to maximise profit over a fixed time frame?

What is the AFL Field Equity Equation? (What is the net expected score from the current game state?)

See two-page document attached