Data-driven learning of chaotic dynamical systems using Discrete-Temporal Sobolev Networks.

We introduce the Discrete-Temporal Sobolev Network (DTSN), a neural network loss function that assists dynamical system forecasting by minimizing variational differences between the network output and the training data via a temporal Sobolev norm. This approach is entirely data-driven, architecture agnostic, and does not require derivative information from the estimated system. The DTSN is particularly well suited to chaotic dynamical systems as it minimizes noise in the network output which is crucial for such sensitive systems. For our test cases we consider discrete approximations of the Lorenz-63 system and the Chua circuit. For the network architectures we use the Long Short-Term Memory (LSTM) and the Transformer. The performance of the DTSN is compared with the standard MSE loss for both architectures, as well as with the Physics Informed Neural Network (PINN) loss for the LSTM. The DTSN loss is shown to substantially improve accuracy for both architectures, while requiring less information than the PINN and without noticeably increasing computational time, thereby demonstrating its potential to improve neural network forecasting of dynamical systems.

A Modified PINN Approach for Identifiable Compartmental Models in Epidemiology with Application to COVID-19.

Many approaches using compartmental models have been used to study the COVID-19 pandemic, with machine learning methods applied to these models having particularly notable success. We consider the Susceptible-Infected-Confirmed-Recovered-Deceased (SICRD) compartmental model, with the goal of estimating the unknown infected compartment I, and several unknown parameters. We apply a variation of a "Physics Informed Neural Network" (PINN), which uses knowledge of the system to aid learning. First, we ensure estimation is possible by verifying the model's identifiability. Then, we propose a wavelet transform to process data for the network training. Finally, our central result is a novel modification of the PINN's loss function to reduce the number of simultaneously considered unknowns. We find that our modified network is capable of stable, efficient, and accurate estimation, while the unmodified network consistently yields incorrect values. The modified network is also shown to be efficient enough to be applied to a model with time-varying parameters. We present an application of our model results for ranking states by their estimated relative testing efficiency. Our findings suggest the effectiveness of our modified PINN network, especially in the case of multiple unknown variables.

Current and Possible Future Therapeutic Options for Huntington's Disease.

Huntington's disease (HD) is an autosomal neurodegenerative disease that is characterized by an excessive number of CAG trinucleotide repeats within the huntingtin gene (HTT). HD patients can present with a variety of symptoms including chorea, behavioural and psychiatric abnormalities and cognitive decline. Each patient has a unique combination of symptoms, and although these can be managed using a range of medications and non-drug treatments there is currently no cure for the disease. Current therapies prescribed for HD can be categorized by the symptom they treat. These categories include chorea medication, antipsychotic medication, antidepressants, mood stabilizing medication as well as non-drug therapies. Fortunately, there are also many new HD therapeutics currently undergoing clinical trials that target the disease at its origin; lowering the levels of mutant huntingtin protein (mHTT). Currently, much attention is being directed to antisense oligonucleotide (ASO) therapies, which bind to pre-RNA or mRNA and can alter protein expression via RNA degradation, blocking translation or splice modulation. Other potential therapies in clinical development include RNA interference (RNAi) therapies, RNA targeting small molecule therapies, stem cell therapies, antibody therapies, non-RNA targeting small molecule therapies and neuroinflammation targeted therapies. Potential therapies in pre-clinical development include Zinc-Finger Protein (ZFP) therapies, transcription activator-like effector nuclease (TALEN) therapies and clustered regularly interspaced short palindromic repeats (CRISPR)/CRISPR-associated system (Cas) therapies. This comprehensive review aims to discuss the efficacy of current HD treatments and explore the clinical trial progress of emerging potential HD therapeutics.