Probabilistic inversion within a multiple‐point statistics framework is often computationally prohibitive for high‐dimensional problems. To partly address this, we introduce and evaluate a new training‐image based inversion approach for complex geologic media. Our approach relies on a deep neural network of the generative adversarial network (GAN) type. After training using a training image (TI), our proposed spatial GAN (SGAN) can quickly generate 2‐D and 3‐D unconditional realizations. A key characteristic of our SGAN is that it defines a (very) low‐dimensional parameterization, thereby allowing for efficient probabilistic inversion using state‐of‐the‐art Markov chain Monte Carlo (MCMC) methods. In addition, available direct conditioning data can be incorporated within the inversion. Several 2‐D and 3‐D categorical TIs are first used to analyze the performance of our SGAN for unconditional geostatistical simulation. Training our deep network can take several hours. After training, realizations containing a few millions of pixels/voxels can be produced in a matter of seconds. This makes it especially useful for simulating many thousands of realizations (e.g., for MCMC inversion) as the relative cost of the training per realization diminishes with the considered number of realizations. Synthetic inversion case studies involving 2‐D steady state flow and 3‐D transient hydraulic tomography with and without direct conditioning data are used to illustrate the effectiveness of our proposed SGAN‐based inversion. For the 2‐D case, the inversion rapidly explores the posterior model distribution. For the 3‐D case, the inversion recovers model realizations that fit the data close to the target level and visually resemble the true model well.

Efficient and high-fidelity prior sampling and inversion for complex geological media is still a largely unsolved challenge. Here, we use a deep neural network of the variational autoencoder type to construct a parametric low-dimensional base model parameterization of complex binary geological media. For inversion purposes, it has the attractive feature that random draws from an uncorrelated standard normal distribution yield model realizations with spatial characteristics that are in agreement with the training set. In comparison with the most commonly used parametric representations in probabilistic inversion, we find that our dimensionality reduction (DR) approach outperforms principle component analysis (PCA), optimization-PCA (OPCA) and discrete cosine transform (DCT) DR techniques for unconditional geostatistical simulation of a channelized prior model. For the considered examples, important compression ratios (200 -500) are achieved. Given that the construction of our parameterization requires a training set of several tens of thousands of prior model realizations, our DR approach is more suited for probabilistic (or deterministic) inversion than for unconditional (or point-conditioned) geostatistical simulation. Probabilistic inversions of 2D steady-state and 3D transient hydraulic tomography data are used to demonstrate the DR-based inversion. For the 2D case study, the performance is superior compared to current state-of-theart multiple-point statistics inversion by sequential geostatistical resampling (SGR).

This study investigated the functional intra-individual movement variability of ice climbers differing in skill level to understand how icefall properties were used by participants as affordances to adapt inter-limb coordination patterns during performance. Seven expert climbers and seven beginners were observed as they climbed a 30 m icefall. Movement and positioning of the left and right hand ice tools, crampons and the climber’s pelvis over the first 20 m of the climb were recorded and digitized using video footage from a camera (25 Hz) located perpendicular to the plane of the icefall. Inter-limb coordination, frequency and types of action and vertical axis pelvis displacement exhibited by each climber were analysed for the first five minutes of ascent. Participant perception of climbing affordances was assessed through: (i) calculating the ratio between exploratory movements and performed actions, and (ii), identifying, by self-confrontation interviews, the perceptual variables of environmental properties, which were significant to climbers for their actions. Data revealed that experts used a wider range of upper and lower limb coordination patterns, resulting in the emergence of different types of action and fewer exploratory movements, suggesting that effective holes in the icefall provided affordances to regulate performance. In contrast, beginners displayed lower levels of functional intra-individual variability of motor organization, due to repetitive swinging of ice tools and kicking of crampons to achieve and maintain a deep anchorage, suggesting lack of perceptual attunement and calibration to environmental properties to support climbing performance.

This study investigated a new performance indicator to assess climbing fluency (smoothness of the hip trajectory and orientation of a climber using normalized jerk coefficients) to explore effects of practice and hold design on performance. Eight experienced climbers completed four repetitions of two, 10-m high routes with similar difficulty levels, but varying in hold graspability (holds with one edge vs holds with two edges). An inertial measurement unit was attached to the hips of each climber to collect 3D acceleration and 3D orientation data to compute jerk coefficients. Results showed high correlations (r = .99, P < .05) between the normalized jerk coefficient of hip trajectory and orientation. Results showed higher normalized jerk coefficients for the route with two graspable edges, perhaps due to more complex route finding and action regulation behaviors. This effect decreased with practice. Jerk coefficient of hip trajectory and orientation could be a useful indicator of climbing fluency for coaches as its computation takes into account both spatial and temporal parameters (ie, changes in both climbing trajectory and time to travel this trajectory).

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Global probabilistic inversion within the latent space learned by a Generative Adversarial Network (GAN) has been recently demonstrated. Compared to inversion on the original model space, using the latent space of a trained GAN can offer the following benefits: (1) the generated model proposals are geostatistically consistent with the prescribed prior training image (TI), and (2) the parameter space is reduced by orders of magnitude compared to the original model space. Nevertheless, exploring the learned latent space by state-of-the-art Markov chain Monte Carlo (MCMC) methods may still require a large computational effort. As an alternative, parameters in this latent space could possibly be optimized with much less computationally expensive gradient-based methods. This study shows that due to the typically highly nonlinear relationship between the latent space and the associated output space of a GAN, gradient-based deterministic inversion may fail even when considering a linear forward physical model. We tested two deterministic inversion approaches: a quasi-Newton gradient descent using the Adam algorithm and a Gauss-Newton (GN) method that makes use of the Jacobian matrix calculated by finite-differencing. For a channelized binary TI and a synthetic linear crosshole ground penetrating radar (GPR) tomography problem involving 576 measurements with low noise, we observe that when allowing for a total of 10,000 iterations only 13% of the gradient descent trials locate a solution that has the required data misfit. The tested GN inversion was unable to recover a solution with the appropriate data misfit. Our results suggest that deterministic inversion performance strongly depends on the inversion approach, starting model, true reference model, number of iterations and noise realization. In contrast, computationally-expensive probabilistic global optimization based on differential evolution always finds an appropriate solution.

Abstract-This paper presents a novel application of a machine learning method to automatically detect and classify climbing activities using inertial measurement units (IMUs) attached to the wrists, feet, and pelvis of the climber. This detection/classification can be useful for research in sport science to replace manual annotation where IMUs are becoming common. Detection requires a learning phase with manual annotation to construct statistical models. Full-body activity is then classified based on the detection of each IMU.