Predicting individual cases of major adolescent psychiatric conditions with artificial intelligence.

Three-quarters of lifetime mental illness occurs by the age of 24, but relatively little is known about how to robustly identify youth at risk to target intervention efforts known to improve outcomes. Barriers to knowledge have included obtaining robust predictions while simultaneously analyzing large numbers of different types of candidate predictors. In a new, large, transdiagnostic youth sample and multidomain high-dimension data, we used 160 candidate predictors encompassing neural, prenatal, developmental, physiologic, sociocultural, environmental, emotional and cognitive features and leveraged three different machine learning algorithms optimized with a novel artificial intelligence meta-learning technique to predict individual cases of anxiety, depression, attention deficit, disruptive behaviors and post-traumatic stress. Our models tested well in unseen, held-out data (AUC ≥ 0.94). By utilizing a large-scale design and advanced computational approaches, we were able to compare the relative predictive ability of neural versus psychosocial features in a principled manner and found that psychosocial features consistently outperformed neural metrics in their relative ability to deliver robust predictions of individual cases. We found that deep learning with artificial neural networks and tree-based learning with XGBoost outperformed logistic regression with ElasticNet, supporting the conceptualization of mental illnesses as multifactorial disease processes with non-linear relationships among predictors that can be robustly modeled with computational psychiatry techniques. To our knowledge, this is the first study to test the relative predictive ability of these gold-standard algorithms from different classes across multiple mental health conditions in youth within the same study design in multidomain data utilizing >100 candidate predictors. Further research is suggested to explore these findings in longitudinal data and validate results in an external dataset.

Structured time-delay models for dynamical systems with connections to Frenet-Serret frame.

Time-delay embedding and dimensionality reduction are powerful techniques for discovering effective coordinate systems to represent the dynamics of physical systems. Recently, it has been shown that models identified by dynamic mode decomposition on time-delay coordinates provide linear representations of strongly nonlinear systems, in the so-called Hankel alternative view of Koopman (HAVOK) approach. Curiously, the resulting linear model has a matrix representation that is approximately antisymmetric and tridiagonal; for chaotic systems, there is an additional forcing term in the last component. In this paper, we establish a new theoretical connection between HAVOK and the Frenet-Serret frame from differential geometry, and also develop an improved algorithm to identify more stable and accurate models from less data. In particular, we show that the sub- and super-diagonal entries of the linear model correspond to the intrinsic curvatures in the Frenet-Serret frame. Based on this connection, we modify the algorithm to promote this antisymmetric structure, even in the noisy, low-data limit. We demonstrate this improved modelling procedure on data from several nonlinear synthetic and real-world examples.

Sparse identification of nonlinear dynamics for rapid model recovery.

Big data have become a critically enabling component of emerging mathematical methods aimed at the automated discovery of dynamical systems, where first principles modeling may be intractable. However, in many engineering systems, abrupt changes must be rapidly characterized based on limited, incomplete, and noisy data. Many leading automated learning techniques rely on unrealistically large data sets, and it is unclear how to leverage prior knowledge effectively to re-identify a model after an abrupt change. In this work, we propose a conceptual framework to recover parsimonious models of a system in response to abrupt changes in the low-data limit. First, the abrupt change is detected by comparing the estimated Lyapunov time of the data with the model prediction. Next, we apply the sparse identification of nonlinear dynamics (SINDy) regression to update a previously identified model with the fewest changes, either by addition, deletion, or modification of existing model terms. We demonstrate this sparse model recovery on several examples for abrupt system change detection in periodic and chaotic dynamical systems. Our examples show that sparse updates to a previously identified model perform better with less data, have lower runtime complexity, and are less sensitive to noise than identifying an entirely new model. The proposed abrupt-SINDy architecture provides a new paradigm for the rapid and efficient recovery of a system model after abrupt changes.

Classification of birefringence in mode-locked fiber lasers using machine learning and sparse representation.

It has been observed that changes in the birefringence, which are difficult or impossible to directly measure, can significantly affect mode-locking in a fiber laser. In this work we develop techniques to estimate the effective birefringence by comparing a test measurement of a given objective function against a learned library. In particular, a toroidal search algorithm is applied to the laser cavity for various birefringence values by varying the waveplate and polarizer angles at incommensurate angular frequencies, thus producing a time-series of the objective function. The resulting time series, which is converted to a spectrogram and then dimensionally reduced with a singular value decomposition, is then labelled with the corresponding effective birefringence and concatenated into a library of modes. A sparse search algorithm (L(1)-norm optimization) is then applied to a test measurement in order to classify the birefringence of the fiber laser. Simulations show that the sparse search algorithm performs very well in recognizing cavity birefringence even in the presence of noise and/or noisy measurements. Once classified, the wave plates and polarizers can be adjusted using servo-control motors to the optimal positions obtained from the toroidal search. The result is an efficient, self-tuning laser.

Modulational stability of plane waves in nonreturn-to-zero communications systems with dispersion management.

Dispersion-managed optical transmission lines, with dispersion periodically switched between the normal and anomalous regimes, offer significantly better performance than transmission lines with constant dispersion by reducing the dispersion penalty and spectral broadening owing to self-phase modulation. We analyze the evolution of plane waves in a dispersion-managed transmission line, using Floquet theory, and show them to be modulationally stable, provided that the average dispersion is zero or negative (normal dispersion) and that the switching is fast enough, and to be unstable when anomalous dispersion dominates. These results indicate that the transition regions between 1's and 0's are primarily responsible for pulse deformations.