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Hybrid physics-based data-driven models, namely, augmented physics-based models (APBMs), are capable of learning complex state dynamics while maintaining some level of model interpretability that can be controlled through appropriate regularizations of the data-driven component. In this article, we extend the APBM formulation for high-order Markov models, where the state space is further augmented with past states (AG-APBM). Typically, state augmentation is a powerful method for state estimation for a high-order Markov model, but it requires the exact knowledge of the system dynamics. The proposed approach, however, does not require full knowledge of dynamics, especially the Markovity order. To mitigate the extra computational burden of such augmentation we propose an approximated-state APBM (AP-APBM) implementation leveraging summaries from past time steps. We demonstrate the performance of AG- and AP-APBMs in an autoregressive model and a target-tracking scenario based on the trajectory of a controlled aircraft with delay-feedback control. The experiments showed that both proposed strategies outperformed the standard APBM approach in terms of estimation error and that the AP-APBM only degraded slightly when compared to AG-APBM. For example, the autoregressive (AR) model simulation in our settings showed that AG-APBM and AP-APBM reduced the estimate error by 31.1% and 26.7%. The time cost and memory usage were reduced by 37.5% and 20% by AP-APBM compared to AG-APBM. 

Abstract Objective.The RSVP Keyboard is a non-implantable, event-related potential-based brain-computer interface (BCI) system designed to support communication access for people with severe speech and physical impairments. Here we introduce inquiry preview (IP), a new RSVP Keyboard interface incorporating switch input for users with some voluntary motor function, and describe its effects on typing performance and other outcomes.Approach.Four individuals with disabilities participated in the collaborative design of possible switch input applications for the RSVP Keyboard, leading to the development of IP and a method of fusing switch input with language model and electroencephalography (EEG) evidence for typing. Twenty-four participants without disabilities and one potential end user with incomplete locked-in syndrome took part in two experiments investigating the effects of IP and two modes of switch input on typing accuracy and speed during a copy-spelling task.Main results.For participants without disabilities, IP and switch input tended to worsen typing performance compared to the standard RSVP Keyboard condition, with more consistent effects across participants for speed than for accuracy. However, there was considerable variability, with some participants demonstrating improved typing performance and better user experience (UX) with IP and switch input. Typing performance for the potential end user was comparable to that of participants without disabilities. He typed most quickly and accurately with IP and switch input and gave favorable UX ratings to those conditions, but preferred standard RSVP Keyboard.Significance.IP is a novel multimodal interface for the RSVP Keyboard BCI, incorporating switch input as an additional control signal. Typing performance and UX and preference varied widely across participants, reinforcing the need for flexible, customizable BCI systems that can adapt to individual users. ClinicalTrials.gov Identifier: NCT04468919.