General Method for the Dimension Reduction of Adaptive Control Experiments

Abstract

Adaptive femtosecond control experiments are expanding the possibilities for using laser pulses as photophysical and photochemical reagents. However, because of the large number of variables necessary to perform these experiments (usually 100-200), it has proven difficult to elucidate the underlying control mechanisms from the optimized pulse shapes. If adaptive control is to become a widespread tool for examining chemical dynamics, methods must be developed that reveal latent control mechanisms. This manuscript presents a generally applicable method for dimension reduction of adaptive control experiments based on partial least squares regression analysis (PLS) of the normalized covariance matrix of the total data set. When applied to experimental results obtained in our laboratory, it shows that only seven fundamental dimensions from an original 208-dimension search space are needed to account for approximately 90% of the variance in the observed fitness of 11,700 laser-pulse shapes explored during the optimization experiment. Furthermore, the seven dimensions have a remarkable regularity in their functional form. It is anticipated that this work will facilitate theoretical treatments directly linking the optimal fields to control mechanisms, allow quantitative comparisons of independent control results, and suggest new experimental methods for rapid adaptive searches.

Assessment of optimal control mechanism complexity by experimental landscape Hessian analysis: fragmentation of CH2BrI

“…The challenge in understanding the mechanism is tied to the common situation of operating with a large number of control variables and the nonlinearity of the dynamics with respect to the field. In some cases, prior knowledge of the system has permitted expressing the control in terms of a small number of parameters, and principal component analysis [7,8] has found use in seeking a basis set of control variables with reduced dimensionality [9][10][11]. An overall goal is to gain knowledge about the effective complexity of the quantum system expressed in terms of the nature of the participating states under control, which is often not easily deduced from the nominal experimental data.…”

Enhanced Triplet Formation in Polycrystalline Tetracene Films by Femtosecond Optical-Pulse Shaping

“…For unshaped pulse experiments [30 fs FWHM via autocorrelation; near transform limited (TL)] a constant phase was sent to the shaper, while for pulse shaping experiments a threeparameter phase function was used (see below). The adaptive algorithm uses evolutionary strategies described in detail elsewhere [15]. A portion of the absorption spectrum of the film used, is shown in Fig.…”

Controlling Vibrational Excitation with Shaped Mid-IR Pulses

“…Using the probe spectrum for feedback, a i , b i , and c i were optimized using an evolutionary algorithm to find the best coefficients for the desired outcome [12]. This basis set was chosen to approximate the pulse shapes that Meier and Heitz predicted would optimize the vibrational excitation of the metal carbonyl in carboxyhemoglobin [9] while simultaneously limiting the dimensions of the control space [13]. We found that four sine waves were the fewest necessary to achieve the desired optimization.…”