Sparse Sampling Research Articles

Spatio-temporal modeling of satellite-observed CO2 columns in China using deep learning

Satellite measurements of the column-averaged dry air mole fraction of atmospheric carbon dioxide (XCO2) play a crucial role in monitoring CO2 emissions and sinks. However, the current limitations of satellite observations, including sparse sampling, narrow swath coverage, and data gaps caused by factors like clouds, significantly hinder their ability to accurately capture local-scale CO2 sources and sinks. This study introduces an innovative data-driven approach based on deep learning, which takes into consideration both spatial and temporal variations, to map XCO2 using observations from multiple satellites. By leveraging advanced deep learning techniques like conventional neural network (CNN), long short-term memory network (LSTM), channel-spatial attention, and artificial neural network (ANN) in the model training, this approach not only incorporates spatiotemporal variations of XCO2 but also integrates information from related terrestrial, anthropogenic, and meteorological variables. The results demonstrate a notable improvement in the predictive capability of the approach. An important advancement over previous studies is that this approach breaks away from the conventional practice of using model-generated XCO2 simulations for both training and validation. Monthly deep-learning XCO2 (DL-XCO2) of China from 2014 to 2022 was generated with a spatial resolution of 0.25° based on satellite retrievals from GOSAT and OCO-2/3. Cross-validation results show an average prediction bias of −0.16 ppm. Additionally, DL-XCO2 exhibits high precision when compared to two TCCON stations, with errors of 0.93 and 1.29 ppm in Hefei and Xianghe, respectively. Ultimately, the DL-XCO2 data effectively capture urban CO2 variations, showcasing the potential in accurately characterizing fine-scale CO2 sources and sinks.

Color image sparse adversarial samples generation via color channel Volterra expansion

Color image sparse adversarial samples generation via color channel Volterra expansion

Normalized weighted cross correlation for multi-channel image registration

The normalized cross-correlation (NCC) is widely used for image registration due to its simple geometrical interpretation and being feature-agnostic. Here, after reviewing NCC definitions for images with an arbitrary number of dimensions and channels, we propose a generalization in which each pixel value of each channel can be individually weighted using real non-negative numbers. This generalized normalized weighted cross-correlation (NWCC) and its zero-mean equivalent (ZNWCC) can be used, for example, to prioritize pixels based on signal-to-noise ratio. Like a previously defined NWCC with binary weights, the proposed generalizations enable the registration of uniformly, but not necessarily isotropically, sampled images with irregular boundaries and/or sparse sampling. All NCC definitions discussed here are provided with discrete Fourier transform (DFT) formulations for fast computation. Practical aspects of NCC computational implementation are briefly discussed, and a convenient function to calculate the overlap of uniformly, but not necessarily isotropically, sampled images with irregular boundaries and/or sparse sampling is introduced, together with its DFT formulation. Finally, examples illustrate the benefit of the proposed normalized cross-correlation functions.

Selective Sparse Sampling of Water Droplets in Oil with Acoustic Tweezers.

In microfluidics, water droplets are often used as independent biochemical microreactor units, enabling the implementation of massively parallel screening assays where only a few of the reacting water droplets yield a positive result. However, sampling the product of these few successful reactions is an unsolved challenge. One possible solution is to use acoustic tweezers, which are lab-free, easily miniaturized, and biocompatible manipulation tools, and existing acoustic tweezers manipulating particles or cells, and water droplet manipulation in oil with an acoustic tweezer is absent. The first challenge in attempting to recover a few water droplets from a large batch is the selective manipulation of water droplets in an oil system. In this paper, we trap and manipulate single water droplets in oil using integrated single-beam (focused beam/vortex beam) acoustic tweezers for the first time. We find that water droplets with a diameter smaller than half a wavelength are trapped by acoustic vortices, while larger ones are better captured by focused acoustic beams. It is the first step to extract the target water droplet microreactors (positive ones) in an oil system and analyze their content. Compared to previous techniques, such as fluorescence-activated cell sorting (FACS), our technique is sparse, meaning that the sampling time is proportional to the number of droplets required and very insensitive to the total number of microreactors, making it well suited for large-scale screening assays.

High-Efficiency Dynamic Three-Dimensional Topography Measurement Using the Phase Shift Generation Method

In the fringe projection profilometry (FPP), the traditional phase-shifting (TPS) algorithm and the Fourier transform (FT) algorithm are beset with a conundrum where measurement efficiency and conflicts with measurement accuracy, thereby limiting their application in dynamic three-dimensional (3D) measurements. Here, we propose a phase shift generation (PSG) method, which acquires the sinusoidal fringes by sparse sampling and reconstructs the complete phase-shifting sequence by generating the missing fringes with superimposed coupling of adjacent fringes. According to our proposed PSG method in which the sinusoidal fringe sequence size is about half of the TPS method, meaning that the PSG method will be timesaving in the phase-shifting sequence sampling process. Moreover, because of the utilization of multiframe fringes, our PSG method allows for a more accurate measurement than the FT method. Both simulation and experimental results demonstrate that our proposed PSG method can well balance the measurement accuracy and efficiency with a lower sampling rate, bearing a great potential to be applied in both scientific and industrial areas.

Snapshot Sampling May Not Be Enough to Obtain Robust Estimates for Riverine Microplastic Loads.

Wastewater treatment plants (WWTPs) have been described as key contributors of microplastics (MPs) to aquatic systems, yet temporal fluctuations in MP concentrations and loads downstream are underexplored. This study investigated how different sampling frequencies (hourly, weekly, and monthly) affect MP estimates in a stream linked to a single WWTP. Utilizing fluorescence microscopy and Raman spectroscopy, considerable hourly variations in MP concentrations were discovered, while the polymer composition remained consistent. This temporal variability in MP loads was influenced by MP concentration, discharge rates, or a mix of both. These results show a high uncertainty, as relying on sparse snapshot samples combined with annual discharge data led to significant uncertainties in MP load estimates (over- and/or underestimation of emissions by 3.8 billion MPs annually at this site). Our findings stress the necessity of higher-frequency sampling for better comprehending the hydrodynamic factors influencing MP transport. This improved understanding enables a more accurate quantification of MP dynamics, crucial for downstream impact assessments. Therefore, preliminary reconnaissance campaigns are essential for designing extended, representative site-monitoring programs and ensuring more precise trend predictions on a larger scale.

Spatial mapping of key plant functional traits in terrestrial ecosystems across China

Abstract. Trait-based approaches are of increasing concern in predicting vegetation changes and linking ecosystem structures to functions at large scales. However, a critical challenge for such approaches is acquiring spatially continuous plant functional trait maps. Here, six key plant functional traits were selected as they can reflect plant resource acquisition strategies and ecosystem functions, including specific leaf area (SLA), leaf dry matter content (LDMC), leaf N concentration (LNC), leaf P concentration (LPC), leaf area (LA) and wood density (WD). A total of 34 589 in situ trait measurements of 3447 seed plant species were collected from 1430 sampling sites in China and were used to generate spatial plant functional trait maps (∼1 km), together with environmental variables and vegetation indices based on two machine learning models (random forest and boosted regression trees). To obtain the optimal estimates, a weighted average algorithm was further applied to merge the predictions of the two models to derive the final spatial plant functional trait maps. The models showed good accuracy in estimating WD, LPC and SLA, with average R2 values ranging from 0.48 to 0.68. In contrast, both the models had weak performance in estimating LDMC, with average R2 values less than 0.30. Meanwhile, LA showed considerable differences between the two models in some regions. Climatic effects were more important than those of edaphic factors in predicting the spatial distributions of plant functional traits. Estimates of plant functional traits in northeastern China and the Qinghai–Tibetan Plateau had relatively high uncertainties due to sparse samplings, implying a need for more observations in these regions in the future. Our spatial trait maps could provide critical support for trait-based vegetation models and allow exploration of the relationships between vegetation characteristics and ecosystem functions at large scales. The six plant functional trait maps for China with 1 km spatial resolution are now available at https://doi.org/10.6084/m9.figshare.22351498 (An et al., 2023).

Tensor completion-based ISAR imaging with sparse sampling

Tensor completion-based ISAR imaging with sparse sampling

Quantum Control of Radical-Pair Dynamics beyond Time-Local Optimization

We realize arbitrary-wave-form-based control of spin-selective recombination reactions of radical pairs in the low-magnetic-field regime. To this end, we extend the gradient-ascent pulse engineering (GRAPE) paradigm to allow for optimizing reaction yields. This overcomes drawbacks of previously suggested time-local optimization approaches for the reaction control of radical pairs, which were limited to high biasing fields. We demonstrate how efficient time-global optimization of the recombination yields can be realized by gradient-based methods augmented by time blocking, sparse sampling of the yield, and evaluation of the central single time-step propagators and their Fréchet derivatives using iterated Trotter-Suzuki splittings. Results are shown for both a toy model, previously used to demonstrate coherent control of radical-pair reactions in the simpler high-field scenario and, furthermore, for a realistic exciplex-forming donor-acceptor system comprising 16 nuclear spins. This raises prospects for the spin control of actual radical-pair systems in ambient magnetic fields, by suppressing or boosting radical reaction yields using purpose-specific radio-frequency wave forms, paving the way for reaction-yield-dependent quantum magnetometry and potentially applications of quantum control to biochemical radical-pair reactions. We demonstrate the latter aspect for two radical pairs implicated in quantum biology. Published by the American Physical Society 2024

Improved Evolutionary Operators for Sparse Large-Scale Multiobjective Optimization Problems

Many critical science, societal, and engineering fields contain large-scale multiobjective optimization problems (LSMOPs), comprised of many decision variables. However, as the number of decision variables increases, optimization algorithms face exponentially large search spaces, thereby exhibiting a degraded performance. Nonetheless, LSMOPs whose optimal solutions correspond to sparse variable vectors can be solved more efficiently by evolutionary multiobjective optimization (EMO) algorithms. Despite the great recent strides in developing generic EMO algorithms for sparse LSMOPs, there is still room for improvement. Specifically, algorithms still struggle to find convergent and diverse Pareto fronts in an acceptable amount of time when solving sparse LSMOPs with thousands of decision variables. To better solve sparse LSMOPs, we propose a novel set of evolutionary operators to adapt small-scale EMO algorithms for sparse LSMOPs. These simple, novel, and effective operators include varied striped sparse population sampling (VSSPS), sparse simulated binary crossover (S-SBX), and sparse polynomial mutation (S-PM). These operators, combined with NSGA-II, make the proposed S-NSGA-II algorithm. S-NSGA-II runs near-universally faster than existing methods for problems containing up to 6,400 decision variables, while performing as well as or better than contemporary sparse LSMOP algorithms with respect to hypervolume, especially with problems with larger than 5,000 decision variables.

An Application of a Physiologically Based Pharmacokinetic Approach to Predict Ceftazidime Pharmacokinetics in a Pregnant Population.

Physiological changes during pregnancy can alter maternal and fetal drug exposure. The objective of this work was to predict maternal and umbilical ceftazidime pharmacokinetics during pregnancy. Ceftazidime transplacental permeability was predicted from its physicochemical properties and incorporated into the model. Predicted concentrations and parameters from the PBPK model were compared to the observed data. PBPK predicted ceftazidime concentrations in non-pregnant and pregnant subjects of different gestational weeks were within 2-fold of the observations, and the observed concentrations fell within the 5th-95th prediction interval from the PBPK simulations. The calculated transplacental clearance (0.00137 L/h/mL of placenta volume) predicted an average umbilical cord-to-maternal plasma ratio of 0.7 after the first dose, increasing to about 1.0 at a steady state, which also agrees well with clinical observations. The developed maternal PBPK model adequately predicted the observed exposure and kinetics of ceftazidime in the pregnant population. Using a verified population-based PBPK model provides valuable insights into the disposition of drug concentrations in special individuals that are otherwise difficult to study and, in addition, offers the possibility of supplementing sparse samples obtained in vulnerable populations with additional knowledge, informing the dosing adjustment and study design, and improving the efficacy and safety of drugs in target populations.

A multi-fidelity transfer learning strategy based on multi-channel fusion

Multi-fidelity strategies leverage a large amount of low-fidelity data combined with a smaller set of high-fidelity data, thereby achieving satisfactory results at a reasonable cost. In our research, we introduce an innovative multi-fidelity strategy that integrates the concepts of multi-fidelity data fusion and transfer learning. In the proposed framework, we incorporate auto-encoders and a multi-channel transfer learning strategy, enabling the network model to comprehend the relationship between the low-fidelity and high-fidelity models in both explicit and implicit manners. This approach not only enhances prediction accuracy but also mitigates issues such as overfitting and negative transfer, which may arise in scenarios with sparse samples. Additionally, Bayesian optimization is employed for effective hyperparameter selection. To evaluate and analyze the performance of our proposed method, we present a series of benchmark test cases. Furthermore, we also show the application of the proposed method to engineering problems. Firstly, we consider a parametrized partial differential equation problem, where high-fidelity and low-fidelity data are obtained using exact methods and simplified algorithms, respectively. Subsequently, we extend this strategy to convolutional neural network architectures, specifically addressing a pressure Poisson equation problem. We also explore the effect of the reliability of the low-fidelity data and the number of high-fidelity data on the results. The results show that the proposed method exhibits low requirements in terms of both the reliability of the low-fidelity data and the number of high-fidelity data while maintaining satisfactory accuracy metrics.

Population pharmacokinetics of lumefantrine and its metabolite, desbutyl-lumefantrine, in children under five years of age with malaria

We developed a population pharmacokinetic model to characterize the Pharmacokinetics (PK) of lumefantrine and its active metabolite, desbutyl-lumefantrine, in children under 5 years. Data were available from 55 children treated for uncomplicated falciparum malaria with standard 3-day Artemether- Lumefantrine (AL) regimen. Combined sparse and intense PK sampling strategy was used to obtain venous samples for 28 days. Using NONMEM, a two-compartment linear pharmacokinetic model incorporating lag time with first order absorption characterized the PK of lumefantrine. Desbutyl-lumefantrine PK was also characterized with a two compartment model. Inter-subject variability in apparent Clearance (CL/F) was explained by Body Mass Index (BMI) and age, while weight partially explained variability in apparent volume of distribution of the central compartment (V2/F). Ontogeny in CYP3A4, the isozyme metabolizing lumefantrine, was incorporated into the age component of lumefantrine CL/F model. Incorporation of BMI into CL/F model explained variability due to weight and stunting. For lumefantrine typical inter-compartment clearance (Q/F), CL/F, V2/F for a typical subject weighing 13.0 kg and BMI 16.62 kg/m2 , and apparent volume of distribution of peripheral compartment (V3/F) were 0.176 L/hr, 3.19 L/hr, 28.1 L, and 58.4 L, respectively. Lumefantrine CL/F was higher in children ≤2 year compared to those >2 years, notably decreased with increasing BMI (-1.10) and age from two to just less than five years (CL/FAGE: -0.423 (-0.648, -0.198)). Results indicate lumefantrine CL/F is a function of age and BMI. Our findings provide structural basis for future evaluation of rational AL dosing guidelines among under five year olds.

A 3D-Sparse A* autonomous recovery path planning algorithm for Unmanned Surface Vehicle

Thanks to the development of marine intelligent technology and equipment, the Unmanned Surface Vehicle (USV) has been brought into focus for its exceptional application. To overcome the challenge of the stern ramp recovery for USVs, an advanced 3D-Sparse A* path planning algorithm has been proposed. This algorithm incorporated sparse sampling and the time dimension to optimize the generation of waypoints, resulting in a smaller computation load. Dynamic constraints and evaluation functions were integrated to reconstruct the algorithm’s framework. Simulations suggest that planning speed can be increased by a factor of 20, improving recovery efficiency. The path’s smoothness was elevated, with a maximum curvature 50% lower than the original version. Furthermore, the malposition was reduced to 54.78% of the original, meeting the requirements for particular attitude adjustment during stern ramp recovery. Field experiment indicates that the actual results have a maximum velocity deviation of 0.61 m/s and a maximum course deviation of 1.61 m compared to the planning results. The 3D-Sparse A* algorithm can complete the recovery within a distance of 100 m in 60 s, assuming an unobstructed trajectory. This verifies the feasibility and planning efficiency of the algorithm.

Learn the Force We Can: Enabling Sparse Motion Control in Multi-Object Video Generation

We propose a novel unsupervised method to autoregressively generate videos from a single frame and a sparse motion input. Our trained model can generate unseen realistic object-to-object interactions. Although our model has never been given the explicit segmentation and motion of each object in the scene during training, it is able to implicitly separate their dynamics and extents. Key components in our method are the randomized conditioning scheme, the encoding of the input motion control, and the randomized and sparse sampling to enable generalization to out of distribution but realistic correlations. Our model, which we call YODA, has therefore the ability to move objects without physically touching them. Through extensive qualitative and quantitative evaluations on several datasets, we show that YODA is on par with or better than state of the art video generation prior work in terms of both controllability and video quality.

Abstract 7172: Pharmacokinetic/biomarker (PK/BMx) analysis of the toll-like receptor 7 and 8 (TLR7/8) agonist EIK1001 in phase 1 studies in participants (Pts) with solid tumors

Abstract Introduction: Immune checkpoint inhibitors (ICIs) relieve immunosuppression of tumor-reactive T cells and enhance antitumor immune response; however, not all patients benefit and some become refractory. EIK1001 is a TLR7/8 agonist that stimulates myeloid and plasmacytoid dendritic cells, activating immune and inflammatory responses. This dual activity provides another pathway, distinct from effects on checkpoint proteins, to enhance antitumor T-cell activity alone or in combination with ICIs. Methods: Adults with advanced solid tumors received a range of doses of EIK1001 (QW IV) alone and in combination with pembrolizumab (200 mg Q3W; NCT03486301) or atezolizumab (1200 mg Q3W; NCT04196530) in Phase 1 studies (n=128). PK samples were collected on Cycle 1 Day 1 (C1D1) and C1D8 predose and at 0.5, 1, 2, 4, 6, 8, 12, and 24 hrs postdose, with sparse sampling thereafter. Matched cytokine BMx samples were collected. The PK analysis population comprised pts with at least one measurable EIK1001 concentration (1563 observations from 94 pts). PK data were analyzed using non-linear mixed effects in Phoenix (v8.3). Covariate effects of the combination drugs were tested using a stepwise approach with a significance level of 0.05 for forward addition. All other covariates were evaluated using exploratory plots and formally tested using a full matrix approach. Empirical Bayes estimates were used to generate individual steady-state concentration-time profiles and calculate post-hoc PK parameters. Exploratory analyses of exposure-safety and exposure-efficacy were conducted. Results: EIK1001 PK was linear and dose-proportional over the doses studied. Tmax ranged from 4-12 hrs with no accumulation. Pop-PK analysis indicated that body size influenced clearance, but intrinsic factors of age, gender, tumor type, ECOG status, or hepatic/renal impairment (mild/moderate) did not. Combination drugs did not influence clearance. These attributes support BSA-based dosing and inform inclusion/exclusion criteria for future studies. On C1D1, time-dependent increases in IL-6, IL-8, IFNγ, and IP-10 returned to baseline within 24 hrs. An earlier IL-8 increase (Tmax 3-5 hr) is consistent with TLR8 activation on various cells including neutrophils, whereas the delayed increase of IFNγ/IP-10 (Tmax 5-8 hr) suggests a downstream effect. Dose-dependent increases in cytokines were observed, with median peak changes from baseline of 1.13- to 7.97-fold for IFNγ and 0.63- to 12.1-fold for IP-10. The 2 highest doses provided evidence of robust target engagement alone or in combination. Conclusion: The linear, dose-proportional PK of EIK1001 is well described by the Pop-PK model. Increases in IFNγ and IP-10 were consistent with the anticipated mechanism of action, with doses representing target engagement identified. Further development of EIK1001 is underway. Citation Format: Drew Rasco, Manish Patel, Melissa Johnson, Anthony Tolcher, David Sommerhalder, Omid Hamid, Angela Alistar, Jarema Kochan, Etah Kurland, Meihua Wang, Carolyn Cho, Sam Rebello. Pharmacokinetic/biomarker (PK/BMx) analysis of the toll-like receptor 7 and 8 (TLR7/8) agonist EIK1001 in phase 1 studies in participants (Pts) with solid tumors [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2024; Part 1 (Regular Abstracts); 2024 Apr 5-10; San Diego, CA. Philadelphia (PA): AACR; Cancer Res 2024;84(6_Suppl):Abstract nr 7172.

Regional 3D geological modeling along metro lines based on stacking ensemble model

This paper presents a regional 3D geological modeling method based on the stacking ensemble technique to overcome the challenges of sparse borehole data in large-scale linear underground projects. The proposed method transforms the 3D geological modeling problem into a stratigraphic property classification problem within a subsurface space grid cell framework. Borehole data is pre-processed and trained using stacking method with five different machine learning algorithms. The resulting modelled regional cells are then classified, forming a regional 3D grid geological model. A case study for an area of 324 km2 along Xuzhou metro lines is presented to demonstrate the effectiveness of the proposed model. The study shows an overall prediction accuracy of 85.4%. However, the accuracy for key stratigraphy layers influencing the construction risk, such as karst carve strata, is only 4.3% due to the limited borehole data. To address this issue, an oversampling technique based on the synthetic minority oversampling technique (SMOTE) algorithm is proposed. This technique effectively increases the number of sparse stratigraphic samples and significantly improves the prediction accuracy for karst caves to 65.4%. Additionally, this study analyzes the impact of sampling distance on model accuracy. It is found that a lower sampling interval results in higher prediction accuracy, but also increases computational resources and time costs. Therefore, in this study, an optimal sampling distance of 1 m is chosen to balance prediction accuracy and computation cost. Furthermore, the number of geological strata is found to have a negative effect on prediction accuracy. To mitigate this, it is recommended to merge less significant stratigraphy layers, reducing computation time. For key strata layers, such as karst caves, which have a significant impact on construction risk, further on-site sampling or oversampling using the SMOTE technique is recommended.

More Quickly-RRT*: Improved Quick Rapidly-exploring Random Tree Star algorithm based on optimized sampling point with better initial solution and convergence rate

RRT* (Rapidly-exploring Random Tree Star), as a variant of RRT (Rapidly-exploring Random Tree), is widely used to solve path planning problems because of its asymptotic optimality. However, the algorithm is inefficient due to the high initial path cost and the slow convergence rate. In this paper, we propose a More Quickly-RRT* (MQ-RRT*) path planning algorithm based on optimized sampling points to solve the problems. A sparse sampling mechanism is proposed in MQ-RRT* to improve the global search efficiency by reducing repetitive sampling. To make the random tree oriented when expanding, a dynamic goal-biased strategy is proposed, which can reduce the sampling time. Like Q-RRT* (Quick-RRT*), MQ-RRT* expands the set of possible parent nodes in the ChooseParent and Rewire phases, which reduces the path cost. On this basis, a method for creating a new parent node close to the obstacle is proposed. The creation process can be divided into two steps: Remove-tips and CreateNodes, which further reduces the cost of path generation and makes the path smoother by using the triangle inequality principle. Finally, numerical simulations are used to compare the proposed algorithm with RRT*, Q-RRT*, GuILD (Guided Incremental Local Densification), and F-RRT* (Fast-RRT*), which verifies that the proposed algorithm has certain advantages in path cost, convergence rate, and path smoothness.

Class Activation Maps-based Feature Augmentation for long-tailed classification

It remains an important and challenging problem for the classification of long-tailed data. Most existing methods focus on sampling strategies based on tail classes. However, adequately representing tail classes becomes challenging when they contain only a few sparse samples, leading to difficulty in capturing accurate decision boundaries. To deal with this problem, we propose a Layer Class Activation Map for feature augmentation (LayerCAM-FA) method. The core of our method is to make full use of the knowledge of head classes to augment the features of tail classes. First, the layer-class activation map is employed to capture the features learned from a network which is most useful for identifying the label. The extracted features are decomposed into two parts: distinctive features and common features. The distinctive features pay more attention to recognizing the label, and the common features concentrate on generalized information of different classes. Then, some head classes with similar characteristics to tail classes are selected by attribute and probability distance to augment the features of tail classes. Finally, the distinctive features of tail classes are combined with the common features of head classes to augment the features of tail classes, and the augmented features are used to fine-tune the network to obtain the final classification result. The effectiveness of our proposed LayerCAM-FA is demonstrated using experimental results compared with other related methods.

Deep-NCA: A deep learning methodology for performing noncompartmental analysis of pharmacokinetic data.

Noncompartmental analysis (NCA) is a model-independent approach for assessing pharmacokinetics (PKs). Although the existing NCA algorithms are very well-established and widely utilized, they suffer from low accuracies in the setting of sparse PK samples. In response, we developed Deep-NCA, a deep learning (DL) model to improve the prediction of key noncompartmental PK parameters. Our methodology utilizes synthetic PK data for model training and uses an innovative patient-specific normalization method for data preprocessing. Deep-NCA demonstrated adequate performance across six previously unseen simulated drugs under multiple dosing, showcasing effective generalization. Compared to traditional NCA, Deep-NCA exhibited superior performance for sparse PK data. This study advances the application of DL to PK studies and introduces an effective method for handling sparse PK data. With further validation and refinement, Deep-NCA could significantly enhance the efficiency of drug development by providing more accurate NCA estimates while requiring fewer PK samples.