A model-based approach to forecasting chaotic dynamical systems utilizes knowledge of the physical processes governing the dynamics to build an approximate mathematical model of the system. In contrast, machine learning techniques have demonstrated promising results for forecasting chaotic systems purely from past time series measurements of system state variables (training data), without prior knowledge of the system dynamics. The motivation for this paper is the potential of machine learning for filling in the gaps in our underlying mechanistic knowledge that cause widely-used knowledge-based models to be inaccurate. Thus we here propose a general method that leverages the advantages of these two approaches by combining a knowledge-based model and a machine learning technique to build a hybrid forecasting scheme. Potential applications for such an approach are numerous (e.g., improving weather forecasting). We demonstrate and test the utility of this approach using a particular illustrative version of a machine learning known as reservoir computing, and we apply the resulting hybrid forecaster to a low-dimensional chaotic system, as well as to a high-dimensional spatiotemporal chaotic system. These tests yield extremely promising results in that our hybrid technique is able to accurately predict for a much longer period of time than either its machine-learning component or its model-based component alone. Prediction of dynamical system states (e.g., as in weather forecasting) is a common and essential task with many applications in science and technology. This task is often carried out via a system of dynamical equations derived to model the process to be predicted. Due to deficiencies in knowledge or computational capacity, application of these models will generally be imperfect and may give unacceptably inaccurate results. On the other hand data-driven methods, independent of derived knowledge of the system, can be computationally intensive and require unreasonably large amounts of data. In this paper we consider a particular hybridization technique for combining these two approaches. Our tests of this hybrid technique suggest that it can be extremely effective and widely applicable.

Natural language processing (NLP) has the capacity to increase the scale and efficiency of content analysis in Physics Education Research. One promise of this approach is the possibility of implementing coding schemes on large data sets taken from diverse contexts. Applying NLP has two main challenges, however. First, a large initial human-coded data set is needed for training, though it is not immediately clear how much training data are needed. Second, if new data are taken from a different context from the training data, automated coding may be impacted in unpredictable ways. In this study, we investigate the conditions necessary to address these two challenges for a survey question that probes students' perspectives on the reliability of physics experimental results. We use neural networks in conjunction with Bag of Words embedding to perform automated coding of student responses for two binary codes, meaning each code is either present or absent in a response. We find that i) substantial agreement is consistently achieved for our data when the training set exceeds 600 responses, with 80-100 responses containing each code and ii) it is possible to perform automated coding using training data from a disparate context, but variation in code frequencies (outcome balances) across specific contexts can affect the reliability of coding. We offer suggestions for best practices in automated coding. Other smaller-scale investigations across a diverse range of coding scheme types and data contexts are needed to develop generalized principles.

No abstract

Research has shown that students in inquiry-based physics labs often expect their experiment to verify a known theory or model, contrary to the goals of the lab. It is important, therefore, to identify ways for instructors to shift students' expectations or epistemic frames to those in line with scientific inquiry. In this paper, we analyze video recordings of one inquiry-based lab session in which the instructor intentionally encourages students to falsify, or disprove, the claim under investigation. We find that students operationalize the instructor's prompt by taking up one of two distinct epistemic frames: open outcome and verification. Students in the open outcome frame initially expect to falsify their claim, but form other conclusions in the face of alternative evidence. Students in the verification frame, however, view falsification as verifying that a claim is false and do not consider other possible outcomes even when they find conflicting data. These results suggest that students may interpret instructor prompts for frame shifts in very different ways. We argue that to shift students to epistemic frames in line with scientific inquiry (e.g., the open outcome frame), instructor prompts should explicitly address uncertainty in outcomes (regarding an experimental result as unknown) and epistemic agency (perceiving oneself as a producer of knowledge).